Permutations: Difference between revisions
→{{header|langur}}
No edit summary |
Langurmonkey (talk | contribs) |
||
(71 intermediate revisions by 26 users not shown) | |||
Line 14:
=={{header|11l}}==
<
L
print(a)
I !a.next_permutation()
L.break</
{{out}}
Line 32:
=={{header|360 Assembly}}==
{{trans|Liberty BASIC}}
<
PERMUTE CSECT
USING PERMUTE,R15 set base register
Line 92:
PG DC CL80' ' buffer
YREGS
END PERMUTE</
{{out}}
<pre style="height:40ex;overflow:scroll">
Line 123:
=={{header|AArch64 Assembly}}==
{{works with|as|Raspberry Pi 3B version Buster 64 bits}}
<syntaxhighlight lang="aarch64 assembly">
/* ARM assembly AARCH64 Raspberry PI 3B */
/* program permutation64.s */
Line 275:
.include "../includeARM64.inc"
</syntaxhighlight>
<pre>
Value : +1
Line 304:
</pre>
=={{header|ABAP}}==
<
lv_number type i,
lt_numbers type table of i.
Line 403:
modify iv_set index lv_perm from lv_temp_2.
modify iv_set index lv_len from lv_temp.
endform.</
{{out}}
<pre>
Line 418:
=={{header|Action!}}==
<
BYTE i
Line 477:
RMARGIN=oldRMARGIN ;restore right margin on the screen
RETURN</
{{out}}
[https://gitlab.com/amarok8bit/action-rosetta-code/-/raw/master/images/Permutations.png Screenshot from Atari 8-bit computer]
Line 509:
===The generic package Generic_Perm===
When given N, this package defines the Element and Permutation types and exports procedures to set a permutation P to the first one, and to change P into the next one:
<
N: positive;
package Generic_Perm is
Line 517:
procedure Set_To_First(P: out Permutation; Is_Last: out Boolean);
procedure Go_To_Next(P: in out Permutation; Is_Last: out Boolean);
end Generic_Perm;</
Here is the implementation of the package:
<
Line 590:
end Go_To_Next;
end Generic_Perm;</
===The procedure Print_Perms===
<
procedure Print_Perms is
Line 622:
when Constraint_Error
=> TIO.Put_Line ("*** Error: enter one numerical argument n with n >= 1");
end Print_Perms;</
{{out}}
Line 635:
=={{header|Aime}}==
<
f1(record r, ...)
{
Line 658:
0;
}</
{{Out}}
<pre>aime permutations -a Aaa Bb C
Line 672:
{{works with|ALGOL 68G|Any - tested with release [http://sourceforge.net/projects/algol68/files/algol68g/algol68g-2.6 algol68g-2.6].}}
{{wont work with|ELLA ALGOL 68|Any (with appropriate job cards) - tested with release [http://sourceforge.net/projects/algol68/files/algol68toc/algol68toc-1.8.8d/algol68toc-1.8-8d.fc9.i386.rpm/download 1.8-8d] - due to extensive use of '''format'''[ted] ''transput''.}}
'''File: prelude_permutations.a68'''<
COMMENT REQUIRED BY "prelude_permutations.a68"
Line 704:
);
SKIP</
# -*- coding: utf-8 -*- #
Line 727:
# OD #))
)</
<pre>
(1, 22, 333, 44444)
Line 757:
=={{header|Amazing Hopper}}==
{{trans|AWK}}
<syntaxhighlight lang="amazing hopper">
/* hopper-JAMBO - a flavour of Amazing Hopper! */
Line 793:
Set(c), [ leng ] Cput(lista)
Return
</syntaxhighlight>
{{out}}
<pre>
Line 806:
=={{header|APL}}==
For Dyalog APL(assumes index origin ⎕IO←1):
<syntaxhighlight lang="apl">
⍝ Builtin version, takes a vector:
⎕CY'dfns'
Line 814:
dpmat←{1=⍵:,⊂,0 ⋄ (⊃,/)¨(⍳⍵)⌽¨⊂(⊂(!⍵-1)⍴⍵-1),⍨∇⍵-1}
perms2←{↓⍵[1+⍉↑dpmat ≢⍵]}
</syntaxhighlight>
<pre>
Line 833:
Recursively, in terms of concatMap and delete:
<
-- permutations :: [a] -> [[a]]
Line 919:
missing value
end if
end uncons</
{{Out}}
<pre>{{"aardvarks", "eat", "ants"}, {"aardvarks", "ants", "eat"},
Line 927:
{{trans|Pseudocode}}
(Fast recursive Heap's algorithm)
<
--> Heaps's algorithm (Permutation by interchanging pairs)
if n = 1 then
Line 968:
DoPermutations(SourceList, SourceList's length)
--> result (value of Permlist)
{"123", "213", "312", "132", "231", "321"}</
===Non-recursive===
As a right fold (which turns out to be significantly faster than recurse + delete):
<
-- permutations :: [a] -> [[a]]
Line 1,104:
{}
end if
end take</
{{Out}}
<pre>{{1, 2, 3}, {2, 1, 3}, {2, 3, 1}, {1, 3, 2}, {3, 1, 2}, {3, 2, 1}}</pre>
Line 1,110:
===Recursive again===
This is marginally faster even than the Pseudocode translation above and doesn't demarcate lists with square brackets, which don't officially exist in AppleScript. It returns the 362,880 permutations of a 9-item list in about a second and a half and the 3,628,800 permutations of a 10-item list in about 16 seconds. Don't let Script Editor attempt to display such large results or you'll have to force-quit it!
<syntaxhighlight lang="applescript">-- Translation of "Improved version of Heap's method (recursive)" found in
-- Robert Sedgewick's PDF document "Permutation Generation Methods"
-- <https://www.cs.princeton.edu/~rs/talks/perms.pdf>
on allPermutations(theList)
script o
-- Work list and precalculated indices for its last four items (assuming that many).
property
property r : (count theList)
property
property
property
-- Output list and traversal index.
property output : {}
property p : 1
-- Recursive handler
on prmt(l)
set rangeLenEven to ((r - l) mod 2 = 1)
-- Tail call elimination repeat.
repeat with l from
prmt(lPlus1)
-- And again after swaps of item l with each of the items to its right
-- (if the range
-- instead be the next iteration of this
if (rangeLenEven) then
repeat with swapIdx from r to (lPlus1 +
tell my workList's item l
set my workList's item l to my workList's item swapIdx
set my workList's item swapIdx to it
end tell
prmt(
end repeat
set
else
set
end tell
prmt(
end repeat
set
end if
tell my workList's item l
set
end tell
set
end repeat
-- Store
--
set
set
set
set my output's item
set
set my output's item
set
set my output's item
set
set my output's item
set
set my output's item (p + 5) to my workList's items
set p to p + 6
end prmt
Line 1,190 ⟶ 1,192:
if (o's r < 3) then
--
copy theList to
if (o's r is 2) then set
else
-- Otherwise
copy theList to o's workList
set factorial to 2
repeat with i from 3 to o's r
end repeat
set o's output to makeList(factorial, missing value)
-- … and call o's recursive handler.
o's prmt(1)
end if
return o's
end allPermutations
on makeList(limit, filler)
if (limit < 1) then return {}
script o
property lst : {filler}
end script
set counter to 1
repeat until (counter + counter > limit)
set o's lst to o's lst & o's lst
set counter to counter + counter
end repeat
if (counter < limit) then set o's lst to o's lst & o's lst's items 1 thru (limit - counter)
return o's lst
end makeList
return allPermutations({1, 2, 3, 4})</syntaxhighlight>
{{output}}
<
=={{header|ARM Assembly}}==
{{works with|as|Raspberry Pi}}
<syntaxhighlight lang="arm assembly">
/* ARM assembly Raspberry PI */
/* program permutation.s */
Line 1,363 ⟶ 1,376:
/***************************************************/
.include "../affichage.inc"
</syntaxhighlight>
<pre>
Value : +1
Line 1,392 ⟶ 1,405:
</pre>
=={{header|Arturo}}==
<
{{out}}
<pre>[1 2 3] [1 3 2] [
=={{header|AutoHotkey}}==
from the forum topic http://www.autohotkey.com/forum/viewtopic.php?t=77959
<
StringCaseSense On
Line 1,446 ⟶ 1,459:
o := A_LoopField o
return o
}</
{{out}}
<pre style="height:40ex;overflow:scroll">Hello
Line 1,511 ⟶ 1,524:
===Alternate Version===
Alternate version to produce numerical permutations of combinations.
<
;1..n = range, or delimited list, or string to parse
; to process with a different min index, pass a delimited list, e.g. "0`n1`n2"
Line 1,543 ⟶ 1,556:
. P(n,k-1,opt,delim,str . A_LoopField . delim)
Return s
}</
{{out}}
<syntaxhighlight lang
<pre style="height:40ex;overflow:scroll">---------------------------
permute.ahk
Line 1,558 ⟶ 1,571:
OK
---------------------------</pre>
<
<pre style="height:40ex;overflow:scroll">---------------------------
permute.ahk
Line 1,607 ⟶ 1,620:
OK
---------------------------</pre>
<
<pre style="height:40ex;overflow:scroll">---------------------------
permute.ahk
Line 1,635 ⟶ 1,648:
OK
---------------------------</pre>
<
<pre style="height:40ex;overflow:scroll">---------------------------
permute.ahk
Line 1,704 ⟶ 1,717:
=={{header|AWK}}==
<syntaxhighlight lang="awk">
# syntax: GAWK -f PERMUTATIONS.AWK [-v sep=x] [word]
#
Line 1,751 ⟶ 1,764:
arr[leng-1] = c
}
</syntaxhighlight>
<p>sample command:</p>
GAWK -f PERMUTATIONS.AWK Gwen
Line 1,759 ⟶ 1,772:
</pre>
=={{header|
==={{header|Applesoft BASIC}}===
{{trans|Commodore BASIC}} Shortened from Commodore BASIC to seven lines. Integer arrays are used instead of floating point. GOTO is used instead of GOSUB to avoid OUT OF MEMORY ERROR due to the call stack being full for values greater than 100.
<syntaxhighlight lang="BASIC"> 10 INPUT "HOW MANY? ";N:J = N - 1
20 S$ = " ":M$ = S$ + CHR$ (13):T = 0: DIM A%(J),K%(J),I%(J),R%(J): FOR I = 0 TO J:A%(I) = I + 1: NEXT :K%(S) = N:R = S:R%(R) = 0:S = S + 1
30 IF K%(R) < = 1 THEN FOR I = 0 TO N - 1: PRINT MID$ (S$,(I = 0) + 1,1)A%(I);: NEXT I:S$ = M$: GOTO 70
40 K%(S) = K%(R) - 1:R%(S) = 0:R = S:S = S + 1: GOTO 30
50 J = I%(R) * (1 - (K%(R) - INT (K%(R) / 2) * 2)):T = A%(J):A%(J) = A%(K%(R) - 1):A%(K%(R) - 1) = T:K%(S) = K%(R) - 1:R%(S) = 1:R = S:S = S + 1: GOTO 30
60 I%(R) = (I%(R) + 1) * R%(S): IF I%(R) < K%(R) - 1 GOTO 50
70 S = S - 1:R = S - 1: IF R > = 0 GOTO 60</syntaxhighlight>
{{Out}}
<pre>HOW MANY? 3
1 2 3
2 1 3
3 1 2
1 3 2
2 3 1
3 2 1
</pre>
<pre>HOW MANY? 4483
?OUT OF MEMORY ERROR IN 20
</pre>
<pre>HOW MANY? 4482
BREAK IN 30
]?FRE(0)
1
</pre>
==={{header|
{{trans|Liberty BASIC}}
<syntaxhighlight lang="basic256">arraybase 1
n = 4 : cont = 0
dim a(n)
dim c(n)
for j = 1 to n
a[j] = j
next j
do
for i = 1 to n
print a[i];
next
print " ";
i = n
cont += 1
if cont = 12 then
print
cont = 0
else
print " ";
end if
do
i -= 1
until (i = 0) or (a[i] < a[i+1])
j = i + 1
k = n
while j < k
tmp = a[j] : a[j] = a[k] : a[k] = tmp
j += 1
k -= 1
end while
if i > 0 then
j = i + 1
while a[j] < a[i]
j += 1
end while
tmp = a[j] : a[j] = a[i] : a[i] = tmp
end if
until i = 0
end</syntaxhighlight>
==={{header|BBC BASIC}}===
The procedure PROC_NextPermutation() will give the next lexicographic permutation of an integer array.
<
List%() = 1, 2, 3, 4
FOR perm% = 1 TO 24
Line 1,863 ⟶ 1,886:
last -= 1
ENDWHILE
ENDPROC</
'''Output:'''
<pre>
Line 1,890 ⟶ 1,913:
4 3 1 2
4 3 2 1
</pre>
==={{header|Commodore BASIC}}===
Heap's algorithm, using a couple extra arrays as stacks to permit recursive calls.
<syntaxhighlight lang="Commodore BASIC">100 INPUT "HOW MANY";N
110 DIM A(N-1):REM ARRAY TO PERMUTE
120 DIM K(N-1):REM HOW MANY ITEMS TO PERMUTE (ARRAY AS STACK)
130 DIM I(N-1):REM CURRENT POSITION IN LOOP (ARRAY AS STACK)
140 S=0:REM STACK POINTER
150 FOR I=0 TO N-1
160 : A(I)=I+1: REM INITIALIZE ARRAY TO 1..N
170 NEXT I
180 K(S)=N:S=S+1:GOSUB 200:REM PERMUTE(N)
190 END
200 IF K(S-1)>1 THEN 270
210 REM PRINT OUT THIS PERMUTATION
220 FOR I=0 TO N-1
230 : PRINT A(I);
240 NEXT I
250 PRINT
260 RETURN
270 K(S)=K(S-1)-1:S=S+1:GOSUB 200:S=S-1:REM PERMUTE(K-1)
280 I(S-1)=0:REM FOR I=0 TO K-2
290 IF I(S-1)>=K(S-1)-1 THEN 340
300 J=I(S-1):IF K(S-1) AND 1 THEN J=0:REM ELEMENT TO SWAP BASED ON PARITY OF K
310 T=A(J):A(J)=A(K(S-1)-1):A(K(S-1)-1)=T:REM SWAP
320 K(S)=K(S-1)-1:S=S+1:GOSUB 200:S=S-1:REM PERMUTE(K-1)
330 I(S-1)=I(S-1)+1:GOTO 290:REM NEXT I
340 RETURN</syntaxhighlight>
{{Out}}
<pre>READY.
RUN
HOW MANY? 3
1 2 3
2 1 3
3 1 2
1 3 2
2 3 1
3 2 1
READY.</pre>
==={{header|Craft Basic}}===
<syntaxhighlight lang="basic">let n = 3
let i = n + 1
dim a[i]
for i = 1 to n
let a[i] = i
next i
do
for i = 1 to n
print a[i]
next i
print
let i = n
do
let i = i - 1
let b = i + 1
loopuntil (i = 0) or (a[i] < a[b])
let j = i + 1
let k = n
do
if j < k then
let t = a[j]
let a[j] = a[k]
let a[k] = t
let j = j + 1
let k = k - 1
endif
loop j < k
if i > 0 then
let j = i + 1
do
if a[j] < a[i] then
let j = j + 1
endif
loop a[j] < a[i]
let t = a[j]
let a[j] = a[i]
let a[i] = t
endif
loopuntil i = 0</syntaxhighlight>
{{out| Output}}<pre>
1 2 3
1 3 2
2 1 3
2 3 1
3 1 2
3 2 1
</pre>
==={{header|FreeBASIC}}===
<syntaxhighlight lang="freebasic">' version 07-04-2017
' compile with: fbc -s console
' Heap's algorithm non-recursive
Sub perms(n As Long)
Dim As ULong i, j, count = 1
Dim As ULong a(0 To n -1), c(0 To n -1)
For j = 0 To n -1
a(j) = j +1
Print a(j);
Next
Print " ";
i = 0
While i < n
If c(i) < i Then
If (i And 1) = 0 Then
Swap a(0), a(i)
Else
Swap a(c(i)), a(i)
End If
For j = 0 To n -1
Print a(j);
Next
count += 1
If count = 12 Then
Print
count = 0
Else
Print " ";
End If
c(i) += 1
i = 0
Else
c(i) = 0
i += 1
End If
Wend
End Sub
' ------=< MAIN >=------
perms(4)
' empty keyboard buffer
While Inkey <> "" : Wend
Print : Print "hit any key to end program"
Sleep
End</syntaxhighlight>
{{out}}
<pre>1234 2134 3124 1324 2314 3214 4213 2413 1423 4123 2143 1243
1342 3142 4132 1432 3412 4312 4321 3421 2431 4231 3241 2341</pre>
==={{header|IS-BASIC}}===
<syntaxhighlight lang="is-basic">100 PROGRAM "Permutat.bas"
110 LET N=4 ! Number of elements
120 NUMERIC T(1 TO N)
130 FOR I=1 TO N
140 LET T(I)=I
150 NEXT
160 LET S=0
170 CALL PERM(N)
180 PRINT "Number of permutations:";S
190 END
200 DEF PERM(I)
210 NUMERIC J,X
220 IF I=1 THEN
230 FOR X=1 TO N
240 PRINT T(X);
250 NEXT
260 PRINT :LET S=S+1
270 ELSE
280 CALL PERM(I-1)
290 FOR J=1 TO I-1
300 LET C=T(J):LET T(J)=T(I):LET T(I)=C
310 CALL PERM(I-1)
320 LET C=T(J):LET T(J)=T(I):LET T(I)=C
330 NEXT
340 END IF
350 END DEF</syntaxhighlight>
==={{header|Liberty BASIC}}===
Permuting numerical array (non-recursive):
{{trans|PowerBASIC}}
<syntaxhighlight lang="lb">
n=3
dim a(n+1) '+1 needed due to bug in LB that checks loop condition
' until (i=0) or (a(i)<a(i+1))
'before executing i=i-1 in loop body.
for i=1 to n: a(i)=i: next
do
for i=1 to n: print a(i);: next: print
i=n
do
i=i-1
loop until (i=0) or (a(i)<a(i+1))
j=i+1
k=n
while j<k
'swap a(j),a(k)
tmp=a(j): a(j)=a(k): a(k)=tmp
j=j+1
k=k-1
wend
if i>0 then
j=i+1
while a(j)<a(i)
j=j+1
wend
'swap a(i),a(j)
tmp=a(j): a(j)=a(i): a(i)=tmp
end if
loop until i=0
</syntaxhighlight>
{{out}}
<pre>
123
132
213
231
312
321
</pre>
Permuting string (recursive):
<syntaxhighlight lang="lb">
n = 3
s$=""
for i = 1 to n
s$=s$;i
next
res$=permutation$("", s$)
Function permutation$(pre$, post$)
lgth = Len(post$)
If lgth < 2 Then
print pre$;post$
Else
For i = 1 To lgth
tmp$=permutation$(pre$+Mid$(post$,i,1),Left$(post$,i-1)+Right$(post$,lgth-i))
Next i
End If
End Function
</syntaxhighlight>
{{out}}
<pre>
123
132
213
231
312
321
</pre>
==={{header|Microsoft Small Basic}}===
{{trans|vba}}
<syntaxhighlight lang="smallbasic">'Permutations - sb
n=4
printem = "True"
For i = 1 To n
p[i] = i
EndFor
count = 0
Last = "False"
While Last = "False"
If printem Then
For t = 1 To n
TextWindow.Write(p[t])
EndFor
TextWindow.WriteLine("")
EndIf
count = count + 1
Last = "True"
i = n - 1
While i > 0
If p[i] < p[i + 1] Then
Last = "False"
Goto exitwhile
EndIf
i = i - 1
EndWhile
exitwhile:
j = i + 1
k = n
While j < k
t = p[j]
p[j] = p[k]
p[k] = t
j = j + 1
k = k - 1
EndWhile
j = n
While p[j] > p[i]
j = j - 1
EndWhile
j = j + 1
t = p[i]
p[i] = p[j]
p[j] = t
EndWhile
TextWindow.WriteLine("Number of permutations: "+count) </syntaxhighlight>
{{out}}
<pre>
1234
1243
1324
1342
1423
1432
2134
2143
2314
2341
2413
2431
3124
3142
3214
3241
3412
3421
4123
4132
4213
4231
4312
4321
Number of permutations: 24
</pre>
==={{header|PowerBASIC}}===
{{works with|PowerBASIC|10.00+}}
<syntaxhighlight lang="ada"> #COMPILE EXE
#DIM ALL
GLOBAL a, i, j, k, n AS INTEGER
GLOBAL d, ns, s AS STRING 'dynamic string
FUNCTION PBMAIN () AS LONG
ns = INPUTBOX$(" n =",, "3") 'input n
n = VAL(ns)
DIM a(1 TO n) AS INTEGER
FOR i = 1 TO n: a(i)= i: NEXT
DO
s = " "
FOR i = 1 TO n
d = STR$(a(i))
s = BUILD$(s, d) ' s & d concatenate
NEXT
? s 'print and pause
i = n
DO
DECR i
LOOP UNTIL i = 0 OR a(i) < a(i+1)
j = i+1
k = n
DO WHILE j < k
SWAP a(j), a(k)
INCR j
DECR k
LOOP
IF i > 0 THEN
j = i+1
DO WHILE a(j) < a(i)
INCR j
LOOP
SWAP a(i), a(j)
END IF
LOOP UNTIL i = 0
END FUNCTION</syntaxhighlight>
{{out}}
<pre>
1 2 3
1 3 2
2 1 3
2 3 1
3 1 2
3 2 1
</pre>
==={{header|PureBasic}}===
The procedure nextPermutation() takes an array of integers as input and transforms its contents into the next lexicographic permutation of it's elements (i.e. integers). It returns #True if this is possible. It returns #False if there are no more lexicographic permutations left and arranges the elements into the lowest lexicographic permutation. It also returns #False if there is less than 2 elemetns to permute.
The integer elements could be the addresses of objects that are pointed at instead. In this case the addresses will be permuted without respect to what they are pointing to (i.e. strings, or structures) and the lexicographic order will be that of the addresses themselves.
<syntaxhighlight lang="purebasic">Macro reverse(firstIndex, lastIndex)
first = firstIndex
last = lastIndex
While first < last
Swap cur(first), cur(last)
first + 1
last - 1
Wend
EndMacro
Procedure nextPermutation(Array cur(1))
Protected first, last, elementCount = ArraySize(cur())
If elementCount < 1
ProcedureReturn #False ;nothing to permute
EndIf
;Find the lowest position pos such that [pos] < [pos+1]
Protected pos = elementCount - 1
While cur(pos) >= cur(pos + 1)
pos - 1
If pos < 0
reverse(0, elementCount)
ProcedureReturn #False ;no higher lexicographic permutations left, return lowest one instead
EndIf
Wend
;Swap [pos] with the highest positional value that is larger than [pos]
last = elementCount
While cur(last) <= cur(pos)
last - 1
Wend
Swap cur(pos), cur(last)
;Reverse the order of the elements in the higher positions
reverse(pos + 1, elementCount)
ProcedureReturn #True ;next lexicographic permutation found
EndProcedure
Procedure display(Array a(1))
Protected i, fin = ArraySize(a())
For i = 0 To fin
Print(Str(a(i)))
If i = fin: Continue: EndIf
Print(", ")
Next
PrintN("")
EndProcedure
If OpenConsole()
Dim a(2)
a(0) = 1: a(1) = 2: a(2) = 3
display(a())
While nextPermutation(a()): display(a()): Wend
Print(#CRLF$ + #CRLF$ + "Press ENTER to exit"): Input()
CloseConsole()
EndIf</syntaxhighlight>
{{out}}
<pre>1, 2, 3
1, 3, 2
2, 1, 3
2, 3, 1
3, 1, 2
3, 2, 1</pre>
==={{header|QBasic}}===
{{works with|QBasic|1.1}}
{{works with|QuickBasic|4.5}}
{{trans|FreeBASIC}}
<syntaxhighlight lang="qbasic">SUB perms (n)
DIM a(0 TO n - 1), c(0 TO n - 1)
FOR j = 0 TO n - 1
a(j) = j + 1
PRINT a(j);
NEXT j
PRINT
i = 0
WHILE i < n
IF c(i) < i THEN
IF (i AND 1) = 0 THEN
SWAP a(0), a(i)
ELSE
SWAP a(c(i)), a(i)
END IF
FOR j = 0 TO n - 1
PRINT a(j);
NEXT j
PRINT
c(i) = c(i) + 1
i = 0
ELSE
c(i) = 0
i = i + 1
END IF
WEND
END SUB
perms(4)</syntaxhighlight>
==={{header|Run BASIC}}===
Works with Run BASIC, Liberty BASIC and Just BASIC
<syntaxhighlight lang="runbasic">list$ = "h,e,l,l,o" ' supply list seperated with comma's
while word$(list$,d+1,",") <> "" 'Count how many in the list
d = d + 1
wend
dim theList$(d) ' place list in array
for i = 1 to d
theList$(i) = word$(list$,i,",")
next i
for i = 1 to d ' print the Permutations
for j = 2 to d
perm$ = ""
for k = 1 to d
perm$ = perm$ + theList$(k)
next k
if instr(perm2$,perm$+",") = 0 then print perm$ ' only list 1 time
perm2$ = perm2$ + perm$ + ","
h$ = theList$(j)
theList$(j) = theList$(j - 1)
theList$(j - 1) = h$
next j
next i
end</syntaxhighlight>Output:
<pre>hello
ehllo
elhlo
ellho
elloh
leloh
lleoh
lloeh
llohe
lolhe
lohle
lohel
olhel
ohlel
ohell
hoell
heoll
helol</pre>
==={{header|True BASIC}}===
{{trans|Liberty BASIC}}
<syntaxhighlight lang="qbasic">SUB SWAP(vb1, vb2)
LET temp = vb1
LET vb1 = vb2
LET vb2 = temp
END SUB
LET n = 4
DIM a(4)
DIM c(4)
FOR i = 1 TO n
LET a(i) = i
NEXT i
PRINT
DO
FOR i = 1 TO n
PRINT a(i);
NEXT i
PRINT
LET i = n
DO
LET i = i - 1
LOOP UNTIL (i = 0) OR (a(i) < a(i + 1))
LET j = i + 1
LET k = n
DO WHILE j < k
CALL SWAP (a(j), a(k))
LET j = j + 1
LET k = k - 1
LOOP
IF i > 0 THEN
LET j = i + 1
DO WHILE a(j) < a(i)
LET j = j + 1
LOOP
CALL SWAP (a(i), a(j))
END IF
LOOP UNTIL i = 0
END</syntaxhighlight>
==={{header|Yabasic}}===
{{trans|Liberty BASIC}}
<syntaxhighlight lang="yabasic">n = 4
dim a(n), c(n)
for j = 1 to n : a(j) = j : next j
repeat
for i = 1 to n: print a(i);: next: print
i = n
repeat
i = i - 1
until (i = 0) or (a(i) < a(i+1))
j = i + 1
k = n
while j < k
tmp = a(j) : a(j) = a(k) : a(k) = tmp
j = j + 1
k = k - 1
wend
if i > 0 then
j = i + 1
while a(j) < a(i)
j = j + 1
wend
tmp = a(j) : a(j) = a(i) : a(i) = tmp
endif
until i = 0
end</syntaxhighlight>
=={{header|Batch File}}==
Recursive permutation generator.
<syntaxhighlight lang="batch file">
@echo off
setlocal enabledelayedexpansion
set arr=ABCD
set /a n=4
:: echo !arr!
call :permu %n% arr
goto:eof
:permu num &arr
setlocal
if %1 equ 1 call echo(!%2! & exit /b
set /a "num=%1-1,n2=num-1"
set arr=!%2!
for /L %%c in (0,1,!n2!) do (
call:permu !num! arr
set /a n1="num&1"
if !n1! equ 0 (call:swapit !num! 0 arr) else (call:swapit !num! %%c arr)
)
call:permu !num! arr
endlocal & set %2=%arr%
exit /b
:swapit from to &arr
setlocal
set arr=!%3!
set temp1=!arr:~%~1,1!
set temp2=!arr:~%~2,1!
set arr=!arr:%temp1%=@!
set arr=!arr:%temp2%=%temp1%!
set arr=!arr:@=%temp2%!
:: echo %1 %2 !%~3! !arr!
endlocal & set %3=%arr%
exit /b
</syntaxhighlight>
{{out}}
<pre>
ABCD
BACD
CABD
ACBD
BCAD
CBAD
DBAC
BDAC
ADBC
DABC
BADC
ABDC
ACDB
CADB
DACB
ADCB
CDAB
DCAB
DCBA
CDBA
BDCA
DBCA
CBDA
BCDA
</pre>
=={{header|Bracmat}}==
<
= prefix List result original A Z
. !arg:(?.)
Line 1,905 ⟶ 2,625:
& !result
)
& out$(perm$(.a 2 "]" u+z);</
Output:
<pre> (a 2 ] u+z.)
Line 1,935 ⟶ 2,655:
===version 1===
Non-recursive algorithm to generate all permutations. It prints objects in lexicographical order.
<syntaxhighlight lang="c">
#include <stdio.h>
int main (int argc, char *argv[]) {
Line 1,990 ⟶ 2,710:
}
}
</syntaxhighlight>
===version 2===
Non-recursive algorithm to generate all permutations. It prints them from right to left.
<syntaxhighlight lang="c">
#include <stdio.h>
Line 2,020 ⟶ 2,740:
}
</syntaxhighlight>
===version 3===
See [[wp:Permutation#Systematic_generation_of_all_permutations|lexicographic generation]] of permutations.
<
#include <stdlib.h>
Line 2,124 ⟶ 2,844:
return 0;
}
</syntaxhighlight>
===version 4===
See [[wp:Permutation#Systematic_generation_of_all_permutations|lexicographic generation]] of permutations.
<
#include <stdlib.h>
Line 2,228 ⟶ 2,948:
return 0;
}
</syntaxhighlight>
=={{header|C sharp|C#}}==
Recursive Linq
{{works with|C sharp|C#|7}}
<
{
public static IEnumerable<IEnumerable<T>> Permutations<T>(this IEnumerable<T> values) where T : IComparable<T>
Line 2,241 ⟶ 2,961:
return values.SelectMany(v => Permutations(values.Where(x => x.CompareTo(v) != 0)), (v, p) => p.Prepend(v));
}
}</
Usage
<
A recursive Iterator. Runs under C#2 (VS2005), i.e. no `var`, no lambdas,...
<
{
public static System.Collections.Generic.IEnumerable<T[]> AllFor(T[] array)
Line 2,275 ⟶ 2,995:
}
}
}</
Usage:
<
{
class Program
Line 2,290 ⟶ 3,010:
}
}
}</
Line 2,296 ⟶ 3,016:
Recursive version
<
class Permutations
{
Line 2,323 ⟶ 3,043:
}
}
}</
Alternate recursive version
<
using System;
class Permutations
Line 2,354 ⟶ 3,074:
}
}
</syntaxhighlight>
[https://en.wikipedia.org/wiki/Heap%27s_algorithm Heap's Algorithm]
<syntaxhighlight lang="csharp">
// Always returns the same array which is the one passed to the function
public static IEnumerable<T[]> HeapsPermutations<T>(T[] array)
{
var state = new int[array.Length];
yield return array;
for (var i = 0; i < array.Length;)
{
if (state[i] < i)
{
var left = i % 2 == 0 ? 0 : state[i];
var temp = array[left];
array[left] = array[i];
array[i] = temp;
yield return array;
state[i]++;
i = 1;
}
else
{
state[i] = 0;
i++;
}
}
}
// Returns a different array for each permutation
public static IEnumerable<T[]> HeapsPermutationsWrapped<T>(IEnumerable<T> items)
{
var array = items.ToArray();
return HeapsPermutations(array).Select(mutating =>
{
var arr = new T[array.Length];
Array.Copy(mutating, arr, array.Length);
return arr;
});
}
</syntaxhighlight>
=={{header|C++}}==
The C++ standard library provides for this in the form of <code>std::next_permutation</code> and <code>std::prev_permutation</code>.
<
#include <string>
#include <vector>
Line 2,397 ⟶ 3,159:
return 0;
}</
{{out}}
<pre>
Line 2,477 ⟶ 3,239:
In an REPL:
<
user=> (require 'clojure.contrib.combinatorics)
nil
user=> (clojure.contrib.combinatorics/permutations [1 2 3])
((1 2 3) (1 3 2) (2 1 3) (2 3 1) (3 1 2) (3 2 1))</
===Explicit===
Replacing the call to the combinatorics library function by its real implementation.
<
(defn- iter-perm [v]
(let [len (count v),
Line 2,522 ⟶ 3,284:
(println (permutations [1 2 3]))
</syntaxhighlight>
=={{header|CoffeeScript}}==
<
# removed from it.
arrayExcept = (arr, idx) ->
Line 2,542 ⟶ 3,304:
# Flatten the array before returning it.
[].concat permutations...</
This implementation utilises the fact that the permutations of an array could be defined recursively, with the fixed point being the permutations of an empty array.
{{out|Usage}}
<
1,2,3
1,3,2
Line 2,551 ⟶ 3,313:
2,3,1
3,1,2
3,2,1</
=={{header|Common Lisp}}==
<
(if list
(mapcan #'(lambda (x)
Line 2,562 ⟶ 3,324:
'(()))) ; else
(print (permute '(A B Z)))</
{{out}}
<pre>((A B Z) (A Z B) (B A Z) (B Z A) (Z A B) (Z B A))</pre>
Lexicographic next permutation:
<
(declare (type (simple-array * (*)) vec))
(macrolet ((el (i) `(aref vec ,i))
Line 2,583 ⟶ 3,345:
;;; test code
(loop for a = "1234" then (next-perm a #'char<) while a do
(write-line a))</
Recursive implementation of Heap's algorithm:
<
(let ((permutations nil))
(labels ((permute (seq k)
Line 2,598 ⟶ 3,360:
(permute seq (1- k)))))))
(permute seq (length seq))
permutations)))</
=={{header|Crystal}}==
<
{{out}}
<pre>[[1, 2, 3], [1, 3, 2], [2, 1, 3], [2, 3, 1], [3, 1, 2], [3, 2, 1]]</pre>
Line 2,607 ⟶ 3,369:
=={{header|Curry}}==
<
insert :: a -> [a] -> [a]
insert x xs = x : xs
Line 2,615 ⟶ 3,377:
permutation [] = []
permutation (x:xs) = insert x $ permutation xs
</syntaxhighlight>
=={{header|D}}==
===Simple Eager version===
Compile with -version=permutations1_main to see the output.
<
T[][] result;
Line 2,640 ⟶ 3,402:
writefln("%(%s\n%)", [1, 2, 3].permutations);
}
}</
{{out}}
<pre>[1, 2, 3]
Line 2,651 ⟶ 3,413:
===Fast Lazy Version===
Compiled with <code>-version=permutations2_main</code> produces its output.
<
struct Permutations(bool doCopy=true, T) if (isMutable!T) {
Line 2,738 ⟶ 3,500:
[B(1), B(2), B(3)].permutations!false.writeln;
}
}</
===Standard Version===
<
import std.stdio, std.algorithm;
Line 2,748 ⟶ 3,510:
items.writeln;
while (items.nextPermutation);
}</
=={{header|Delphi}}==
<
{$APPTYPE CONSOLE}
Line 2,808 ⟶ 3,570:
if Length(S) > 0 then Writeln(S);
Readln;
end.</
{{out}}
<pre>
Line 2,815 ⟶ 3,577:
2341 1342 2143 1243 3124 3214 2314
1324 2134 1234
</pre>
=={{header|EasyLang}}==
<syntaxhighlight lang="easylang">
proc permlist k . list[] .
if k = len list[]
print list[]
return
.
for i = k to len list[]
swap list[i] list[k]
permlist k + 1 list[]
swap list[k] list[i]
.
.
l[] = [ 1 2 3 ]
permlist 1 l[]
</syntaxhighlight>
=={{header|Ecstasy}}==
<syntaxhighlight lang="java">
/**
* Implements permutations without repetition.
*/
module Permutations {
static Int[][] permut(Int items) {
if (items <= 1) {
// with one item, there is a single permutation; otherwise there are no permutations
return items == 1 ? [[0]] : [];
}
// the "pattern" for all values but the first value in each permutation is
// derived from the permutations of the next smaller number of items
Int[][] pattern = permut(items - 1);
// build the list of all permutations for the specified number of items by iterating only
// the first digit
Int[][] result = new Int[][];
for (Int prefix : 0 ..< items) {
for (Int[] suffix : pattern) {
result.add(new Int[items](i -> i == 0 ? prefix : (prefix + suffix[i-1] + 1) % items));
}
}
return result;
}
void run() {
@Inject Console console;
console.print($"permut(3) = {permut(3)}");
}
}
</syntaxhighlight>
{{out}}
<pre>
permut(3) = [[0, 1, 2], [0, 2, 1], [1, 2, 0], [1, 0, 2], [2, 0, 1], [2, 1, 0]]
</pre>
=={{header|EDSAC order code}}==
Uses two subroutines which respectively
(1) Generate the first permutation in lexicographic order;
(2) Return the next permutation in lexicographic order, or set a flag to indicate there are no more permutations.
The algorithm for (2) is the same as in the Wikipedia article "Permutation".
<syntaxhighlight lang="edsac">
[Permutations task for Rosetta Code.]
[EDSAC program, Initial Orders 2.]
T51K P200F [G parameter: start address of subroutines]
T47K P100F [M parameter: start address of main routine]
[====================== G parameter: Subroutines =====================]
E25K TG GK
[Constants used in the subroutines]
[0] AF [add to address to make A order for that address]
[1] SF [add to address to make S order for that address]
[2] UF [(1) add to address to make U order for that address]
[(2) subtract from S order to make T order, same address]
[3] OF [add to A order to make T order, same address]
[-----------------------------------------------------------
Subroutine to initialize an array of n short (17-bit) words
to 0, 1, 2, ..., n-1 (in the address field).
Parameters: 4F = address of array; 5F = n = length of array.
Workspace: 0F, 1F.]
[4] A3F [plant return link as usual]
T19@
A4F [address of array]
A2@ [make U order for that address]
T1F [store U order in 1F]
A5F [load n = number of elements (in address field)]
S2F [make n-1]
[Start of loop; works backwards, n-1 to 0]
[11] UF [store array element in 0F]
A1F [make order to store element in array]
T15@ [plant that order in code]
AF [pick up element fron 0F]
[15] UF [(planted) store element in array]
S2F [dec to next element]
E11@ [loop if still >= 0]
TF [clear acc. before return]
[19] ZF [overwritten by jump back to caller]
[-------------------------------------------------------------------
Subroutine to get next permutation in lexicographic order.
Uses same 4-step algorithm as Wikipedia article "Permutations",
but notation in comments differs from that in Wikipedia.
Parameters: 4F = address of array; 5F = n = length of array.
0F is returned as 0 for success, < 0 if passed-in
permutation is the last.
Workspace: 0F, 1F.]
[20] A3F [plant return link as usual]
T103@
[Step 1: Find the largest index k such that a{k} > a{k-1}.
If no such index exists, the passed-in permutation is the last.]
A4F [load address of a{0}]
A@ [make A order for a{0}]
U1F [store as test for end of loop]
A5F [make A order for a{n}]
U96@ [plant in code below]
S2F [make A order for a{n-1}]
T43@ [plant in code below]
A4F [load address of a{0}]
A5F [make address of a{n}]
A1@ [make S order for a{n}]
T44@ [plant in code below]
[Start of loop for comparing a{k} with a{k-1}]
[33] TF [clear acc]
A43@ [load A order for a{k}]
S2F [make A order for a{k-1}]
S1F [tested all yet?]
G102@ [if yes, jump to failed (no more permutations)]
A1F [restore accumulator after test]
T43@ [plant updated A order]
A44@ [dec address in S order]
S2F
T44@
[43] SF [(planted) load a{k-1}]
[44] AF [(planted) subtract a{k}]
E33@ [loop back if a{k-1} > a{k}]
[Step 2: Find the largest index j >= k such that a{j} > a{k-1}.
Such an index j exists, because j = k is an instance.]
TF [clear acc]
A4F [load address of a{0}]
A5F [make address of a{n}]
A1@ [make S order for a{n}]
T1F [save as test for end of loop]
A44@ [load S order for a{k}]
T64@ [plant in code below]
A43@ [load A order for a{k-1}]
T63@ [plant in code below]
[Start of loop]
[55] TF [clear acc]
A64@ [load S order for a{j} (initially j = k)]
U75@ [plant in code below]
A2F [inc address (in effect inc j)]
S1F [test for end of array]
E66@ [jump out if so]
A1F [restore acc after test]
T64@ [update S order]
[63] AF [(planted) load a{k-1}]
[64] SF [(planted) subtract a{j}]
G55@ [loop back if a{j} still > a{k-1}]
[66]
[Step 3: Swap a{k-1} and a{j}]
TF [clear acc]
A63@ [load A order for a{k-1}]
U77@ [plant in code below, 2 places]
U94@
A3@ [make T order for a{k-1}]
T80@ [plant in code below]
A75@ [load S order for a{j}]
S2@ [make T order for a{j}]
T78@ [plant in code below]
[75] SF [(planted) load -a{j}]
TF [park -a{j} in 0F]
[77] AF [(planted) load a{k-1}]
[78] TF [(planted) store a{j}]
SF [load a{j} by subtracting -a{j}]
[80] TF [(planted) store in a{k-1}]
[Step 4: Now a{k}, ..., a{n-1} are in decreasing order.
Change to increasing order by repeated swapping.]
[81] A96@ [counting down from a{n} (exclusive end of array)]
S2F [make A order for a{n-1}]
U96@ [plant in code]
A3@ [make T order for a{n-1}]
T99@ [plant]
A94@ [counting up from a{k-1} (exclusive)]
A2F [make A order for a{k}]
U94@ [plant]
A3@ [make T order for a{k}]
U97@ [plant]
S99@ [swapped all yet?]
E101@ [if yes, jump to exit from subroutine]
[Swapping two array elements, initially a{k} and a{n-1}]
TF [clear acc]
[94] AF [(planted) load 1st element]
TF [park in 0F]
[96] AF [(planted) load 2nd element]
[97] TF [(planted) copy to 1st element]
AF [load old 1st element]
[99] TF [(planted) copy to 2nd element]
E81@ [always loop back]
[101] TF [done, return 0 in location 0F]
[102] TF [return status to caller in 0F; also clears acc]
[103] ZF [(planted) jump back to caller]
[==================== M parameter: Main routine ==================]
[Prints all 120 permutations of the letters in 'EDSAC'.]
E25K TM GK
[Constants used in the main routine]
[0] P900F [address of permutation array]
[1] P5F [number of elements in permutation (in address field)]
[Array of letters in 'EDSAC', in alphabetical order]
[2] AF CF DF EF SF
[7] O2@ [add to index to make O order for letter in array]
[8] P12F [permutations per printed line (in address field)]
[9] AF [add to address to make A order for that address]
[Teleprinter characters]
[10] K2048F [set letters mode]
[11] !F [space]
[12] @F [carriage return]
[13] &F [line feed]
[14] K4096F [null]
[Entry point, with acc = 0.]
[15] O10@ [set teleprinter to letters]
S8@ [intialize -ve count of permutations per line]
T7F [keep count in 7F]
A@ [pass address of permutation array in 4F]
T4F
A1@ [pass number of elements in 5F]
T5F
[22] A22@ [call subroutine to initialize permutation array]
G4G
[Loop: print current permutation, then get next (if any)]
[24] A4F [address]
A9@ [make A order]
T29@ [plant in code]
S5F [initialize -ve count of array elements]
[28] T6F [keep count in 6F]
[29] AF [(planted) load permutation element]
A7@ [make order to print letter from table]
T32@ [plant in code]
[32] OF [(planted) print letter from table]
A29@ [inc address in permutation array]
A2F
T29@
A6F [inc -ve count of array elements]
A2F
G28@ [loop till count becomes 0]
A7F [inc -ve count of perms per line]
A2F
E44@ [jump if end of line]
O11@ [else print a space]
G47@ [join common code]
[44] O12@ [print CR]
O13@ [print LF]
S8@
[47] T7F [update -ve count of permutations in line]
[48] A48@ [call subroutine for next permutation (if any)]
G20G
AF [test 0F: got a new permutation?]
E24@ [if so, loop to print it]
O14@ [no more, output null to flush teleprinter buffer]
ZF [halt program]
E15Z [define entry point]
PF [enter with acc = 0]
[end]
</syntaxhighlight>
{{out}}
<pre>
ACDES ACDSE ACEDS ACESD ACSDE ACSED ADCES ADCSE ADECS ADESC ADSCE ADSEC
AECDS AECSD AEDCS AEDSC AESCD AESDC ASCDE ASCED ASDCE ASDEC ASECD ASEDC
CADES CADSE CAEDS CAESD CASDE CASED CDAES CDASE CDEAS CDESA CDSAE CDSEA
CEADS CEASD CEDAS CEDSA CESAD CESDA CSADE CSAED CSDAE CSDEA CSEAD CSEDA
DACES DACSE DAECS DAESC DASCE DASEC DCAES DCASE DCEAS DCESA DCSAE DCSEA
DEACS DEASC DECAS DECSA DESAC DESCA DSACE DSAEC DSCAE DSCEA DSEAC DSECA
EACDS EACSD EADCS EADSC EASCD EASDC ECADS ECASD ECDAS ECDSA ECSAD ECSDA
EDACS EDASC EDCAS EDCSA EDSAC EDSCA ESACD ESADC ESCAD ESCDA ESDAC ESDCA
SACDE SACED SADCE SADEC SAECD SAEDC SCADE SCAED SCDAE SCDEA SCEAD SCEDA
SDACE SDAEC SDCAE SDCEA SDEAC SDECA SEACD SEADC SECAD SECDA SEDAC SEDCA
</pre>
=={{header|Eiffel}}==
<syntaxhighlight lang="eiffel">
class
APPLICATION
Line 2,867 ⟶ 3,914:
end
</syntaxhighlight>
{{out}}
<pre>
Line 2,880 ⟶ 3,927:
=={{header|Elixir}}==
{{trans|Erlang}}
<
def permute([]), do: [[]]
def permute(list) do
Line 2,887 ⟶ 3,934:
end
IO.inspect RC.permute([1, 2, 3])</
{{out}}
Line 2,896 ⟶ 3,943:
=={{header|Erlang}}==
Shortest form:
<
-export([permute/1]).
permute([]) -> [[]];
permute(L) -> [[X|Y] || X<-L, Y<-permute(L--[X])].</
Y-combinator (for shell):
<
More efficient zipper implementation:
<
-export([permute/1]).
Line 2,921 ⟶ 3,968:
prepend(_, [], T, R, Acc) -> zipper(T, R, Acc); % continue in zipper
prepend(X, [H|T], ZT, ZR, Acc) -> prepend(X, T, ZT, ZR, [[X|H]|Acc]).</
Demonstration (escript):
<
{{out}}
<pre>[[1,2,3],[1,3,2],[2,1,3],[2,3,1],[3,1,2],[3,2,1]]</pre>
Line 2,929 ⟶ 3,976:
=={{header|Euphoria}}==
{{trans|PureBasic}}
<
object x
while first < last do
Line 2,976 ⟶ 4,023:
end if
puts(1, s & '\t')
end while</
{{out}}
<pre>abcd abdc acbd acdb adbc adcb bacd badc bcad bcda
Line 2,983 ⟶ 4,030:
=={{header|F Sharp|F#}}==
<
let rec insert left x right = seq {
match right with
Line 3,004 ⟶ 4,051:
|> Seq.iter (fun x -> printf "%A\n" x)
0
</syntaxhighlight>
<pre>
Line 3,017 ⟶ 4,064:
Translation of Haskell "insertion-based approach" (last version)
<
let permutations xs =
let rec insert x = function
Line 3,023 ⟶ 4,070:
| head :: tail -> (x :: (head :: tail)) :: (List.map (fun l -> head :: l) (insert x tail))
List.fold (fun s e -> List.collect (insert e) s) [[]] xs
</syntaxhighlight>
=={{header|Factor}}==
Line 3,029 ⟶ 4,076:
=={{header|Fortran}}==
<
implicit none
Line 3,061 ⟶ 4,108:
end subroutine generate
end program permutations</
{{out}}
<pre> 1 2 3
Line 3,075 ⟶ 4,122:
The values need to be "swapped back" after the recursive call.
<
implicit none
integer :: n, i
Line 3,101 ⟶ 4,148:
end if
end subroutine
end program</
Line 3,109 ⟶ 4,156:
Here below is the speed test for a couple of algorithms of permutation. We can add more algorithms into this frame-work. When they work in the same circumstance, we can see which is the fastest one.
<
implicit none
Line 3,469 ⟶ 4,516:
!=====
end program</
An example of performance:
Line 3,524 ⟶ 4,571:
Here is an alternate, iterative version in Fortran 77.
{{trans|Ada}}
<
integer n,i,a
logical nextp
Line 3,564 ⟶ 4,611:
a(j)=t
nextp=.true.
end</
=== Ratfor 77 ===
See [[#RATFOR|RATFOR]].
=={{header|Frink}}==
Frink's array class has built-in methods <CODE>permute[]</CODE> and <CODE>lexicographicPermute[]</CODE> which permute the elements of an array in reflected Gray code order and lexicographic order respectively.
<
println[formatTable[a.lexicographicPermute[]]]</
{{out}}
Line 3,750 ⟶ 4,647:
4 3 2 1
</pre>
=={{header|FutureBasic}}==
=== With recursion ===
Here's a sweet and short solution adapted from Robert Sedgewick's 'Algorithms' (1989, p. 628). It generates its own array of integers.
<syntaxhighlight lang="futurebasic">
void local fn perm( k as Short)
static Short w( 4 ), i = -1
Short j
i ++ : w( k ) = i
if i = 4
for j = 1 to 4 : print w( j ),
next : print
else
for j = 1 to 4 : if w( j ) = 0 then fn perm( j )
next
end if
i -- : w( k ) = 0
end fn
fn perm(0)
handleevents
</syntaxhighlight>
=== With iteration ===
We can also do it by brute force:
<syntaxhighlight lang="futurebasic">
void local fn perm( w as CFStringRef )
Short a, b, c, d
for a = 0 to 3 : for b = 0 to 3 : for c = 0 to 3 : for d = 0 to 3
if a != b and a != c and a != d and b != c and b != d and c != d
print mid(w,a,1); mid(w,b,1); mid(w,c,1); mid(w,d,1)
end if
next : next : next : next
end fn
fn perm (@"abel")
handleevents
</syntaxhighlight>
=={{header|GAP}}==
Line 3,755 ⟶ 4,695:
compute the images of 1 .. n by p. As an alternative, List(SymmetricGroup(n)) would yield the permutations as GAP ''Permutation'' objects,
which would probably be more manageable in later computations.
<
perms(4);
[ [ 1, 2, 3, 4 ], [ 4, 2, 3, 1 ], [ 2, 4, 3, 1 ], [ 3, 2, 4, 1 ], [ 1, 4, 3, 2 ], [ 4, 1, 3, 2 ], [ 2, 1, 3, 4 ],
[ 3, 1, 4, 2 ], [ 1, 3, 4, 2 ], [ 4, 3, 1, 2 ], [ 2, 3, 1, 4 ], [ 3, 4, 1, 2 ], [ 1, 2, 4, 3 ], [ 4, 2, 1, 3 ],
[ 2, 4, 1, 3 ], [ 3, 2, 1, 4 ], [ 1, 4, 2, 3 ], [ 4, 1, 2, 3 ], [ 2, 1, 4, 3 ], [ 3, 1, 2, 4 ], [ 1, 3, 2, 4 ],
[ 4, 3, 2, 1 ], [ 2, 3, 4, 1 ], [ 3, 4, 2, 1 ] ]</
GAP has also built-in functions to get permutations
<
Arrangements([1 .. 4], 4);
# All permutations of 1 .. 4
PermutationsList([1 .. 4]);</
Here is an implementation using a function to compute next permutation in lexicographic order:
<
local i, j, k, n, t;
n := Length(a);
Line 3,810 ⟶ 4,750:
[ [ 1, 2, 3 ], [ 1, 3, 2 ],
[ 2, 1, 3 ], [ 2, 3, 1 ],
[ 3, 1, 2 ], [ 3, 2, 1 ] ]</
=={{header|Glee}}==
<
$$ #s monadic: number of elements in s
$$ ,, monadic: expose with space-lf separators
Line 3,819 ⟶ 4,759:
'Hello' 123 7.9 '•'=>s;
s[s# !! (s#)],,</
Result:
<
Hello 123 • 7.9
Hello 7.9 123 •
Line 3,845 ⟶ 4,785:
• 123 7.9 Hello
• 7.9 Hello 123
• 7.9 123 Hello</
=={{header|GNU make}}==
Line 3,851 ⟶ 4,791:
Recursive on unique elements
<
#delimiter should not occur inside elements
delimiter=;
Line 3,865 ⟶ 4,805:
delimiter_separated_output=$(call permutations,a b c d)
$(info $(delimiter_separated_output))
</syntaxhighlight>
{{out}}
Line 3,874 ⟶ 4,814:
=== recursive ===
<
import "fmt"
Line 3,925 ⟶ 4,865:
}
rc(len(s))
}</
{{out}}
<pre>[1 2 3]
Line 3,936 ⟶ 4,876:
=== non-recursive, lexicographical order ===
<
import "fmt"
Line 3,964 ⟶ 4,904:
fmt.Println(a)
}
}</
{{out}}
Line 3,977 ⟶ 4,917:
=={{header|Groovy}}==
Solution:
<
Test:
<
def permutations = makePermutations(list)
assert permutations.size() == (1..<(list.size()+1)).inject(1) { prod, i -> prod*i }
permutations.each { println it }</
{{out}}
<pre style="height:30ex;overflow:scroll;">[Young, Crosby, Stills, Nash]
Line 4,011 ⟶ 4,951:
=={{header|Haskell}}==
<
main = mapM_ print (permutations [1,2,3])</
A simple implementation, that assumes elements are unique and support equality:
<
permutations :: Eq a => [a] -> [[a]]
permutations [] = [[]]
permutations xs = [ x:ys | x <- xs, ys <- permutations (delete x xs)]</
A slightly more efficient implementation that doesn't have the above restrictions:
<
permutations [] = [[]]
permutations xs = [ y:zs | (y,ys) <- select xs, zs <- permutations ys]
where select [] = []
select (x:xs) = (x,xs) : [ (y,x:ys) | (y,ys) <- select xs ]</
The above are all selection-based approaches. The following is an insertion-based approach:
<
permutations = foldr (concatMap . insertEverywhere) [[]]
where insertEverywhere :: a -> [a] -> [[a]]
insertEverywhere x [] = [[x]]
insertEverywhere x l@(y:ys) = (x:l) : map (y:) (insertEverywhere x ys)</
A serialized version:
{{Trans|Mathematica}}
<syntaxhighlight lang
permutations :: [a] -> [[a]]
permutations =
in foldr
)
[[]]
main :: IO ()
main = print $ permutations [1, 2, 3]</
{{Out}}
<pre>[[1,2,3],[2,3,1],[3,1,2],[2,1,3],[1,3,2],[3,2,1]]</pre>
=={{header|Icon}} and {{header|Unicon}}==
<
every p := permute(A) do every writes((!p||" ")|"\n")
end
Line 4,059 ⟶ 5,003:
if *A <= 1 then return A
suspend [(A[1]<->A[i := 1 to *A])] ||| permute(A[2:0])
end</
{{out}}
<pre>->permute Aardvarks eat ants
Line 4,069 ⟶ 5,013:
ants Aardvarks eat
-></pre>
=={{header|J}}==
<
{{out|Example use}}
<
0 1
1 0
Line 4,110 ⟶ 5,026:
random text some
text some random
text random some</
=={{header|Java}}==
Using the code of Michael Gilleland.
<
private int[] array;
private int firstNum;
Line 4,196 ⟶ 5,112:
}
} // class</
{{out}}
<pre>
Line 4,209 ⟶ 5,125:
Following needs: [[User:Margusmartsepp/Contributions/Java/Utils.java|Utils.java]]
<
public static void main(String[] args) {
System.out.println(Utils.Permutations(Utils.mRange(1, 3)));
}
}</
{{out}}
<pre>[[1, 2, 3], [1, 3, 2], [2, 1, 3], [2, 3, 1], [3, 1, 2], [3, 2, 1]]</pre>
Line 4,222 ⟶ 5,138:
Copy the following as an HTML file and load in a browser.
<
<body><pre id="result"></pre>
<script type="text/javascript">
Line 4,244 ⟶ 5,160:
perm([1, 2, 'A', 4], []);
</script></body></html></
Alternatively: 'Genuine' js code, assuming no duplicate.
<syntaxhighlight lang="javascript">
function perm(a) {
if (a.length < 2) return [a];
Line 4,261 ⟶ 5,177:
console.log(perm(['Aardvarks', 'eat', 'ants']).join("\n"));
</syntaxhighlight>
{{Out}}
<
Aardvarks,ants,eat
eat,Aardvarks,ants
eat,ants,Aardvarks
ants,Aardvarks,eat
ants,eat,Aardvarks</
====Functional composition====
Line 4,277 ⟶ 5,193:
(Simple version – assuming a unique list of objects comparable by the JS === operator)
<
'use strict';
Line 4,311 ⟶ 5,227:
// TEST
return permutations(['Aardvarks', 'eat', 'ants']);
})();</
{{Out}}
<
["eat", "Aardvarks", "ants"], ["eat", "ants", "Aardvarks"],
["ants", "Aardvarks", "eat"], ["ants", "eat", "Aardvarks"]]</
===ES6===
Recursively, in terms of concatMap and delete:
<
'use strict';
Line 4,358 ⟶ 5,274:
permutations(['Aardvarks', 'eat', 'ants'])
);
})();</
{{Out}}
<
["eat", "Aardvarks", "ants"], ["eat", "ants", "Aardvarks"],
["ants", "Aardvarks", "eat"], ["ants", "eat", "Aardvarks"]]</
Or, without recursion, in terms of concatMap and reduce:
<
'use strict';
Line 4,407 ⟶ 5,323:
permutations([1, 2, 3])
);
})();</
{{Out}}
<pre>[[1,2,3],[2,1,3],[2,3,1],[1,3,2],[3,1,2],[3,2,1]]</pre>
Line 4,413 ⟶ 5,329:
=={{header|jq}}==
"permutations" generates a stream of the permutations of the input array.
<
if length == 0 then []
else
Line 4,419 ⟶ 5,335:
| [.[$i]] + (del(.[$i])|permutations)
end ;
</syntaxhighlight>
'''Example 1''': list them
[range(0;3)] | permutations
Line 4,446 ⟶ 5,362:
=={{header|Julia}}==
<syntaxhighlight lang="julia">
julia> perms(l) = isempty(l) ? [l] : [[x; y] for x in l for y in perms(setdiff(l, x))]
</syntaxhighlight>
{{out}}
<syntaxhighlight lang="julia">
julia> perms([1,2,3])
6-element Vector{Vector{Int64}}:
Line 4,459 ⟶ 5,375:
[3, 1, 2]
[3, 2, 1]
</syntaxhighlight>
Further support for permutation creation and processing is available in the <tt>Combinatorics.jl</tt> package.
<tt>permutations(v)</tt> creates an iterator over all permutations of <tt>v</tt>. Julia 0.7 and 1.0+ require the line global i inside the for to update the i variable.
<syntaxhighlight lang="julia">
using Combinatorics
Line 4,478 ⟶ 5,394:
end
println()
</syntaxhighlight>
{{out}}
Line 4,495 ⟶ 5,411:
</pre>
<syntaxhighlight lang="text">
# Generate all permutations of size t from an array a with possibly duplicated elements.
collect(Combinatorics.multiset_permutations([1,1,0,0,0],3))
</syntaxhighlight>
{{out}}
<pre>
Line 4,513 ⟶ 5,429:
=={{header|K}}==
{{trans|J}}
<
perm 2
(0 1
Line 4,524 ⟶ 5,440:
random text some
text some random
text random some</
Alternative:
<syntaxhighlight lang="k">
perm:{x@m@&n=(#?:)'m:!n#n:#x}
Line 4,553 ⟶ 5,469:
text some random
text random some
</syntaxhighlight>
{{works with|ngn/k}}
<syntaxhighlight lang=K> prm:{$[0=x;,!0;,/(prm x-1){?[1+x;y;0]}/:\:!x]}
perm:{x[prm[#x]]}
(("some";"random";"text")
("random";"some";"text")
("random";"text";"some")
("some";"text";"random")
("text";"some";"random")
("text";"random";"some"))</syntaxhighlight>
Note, however that K is heavily optimized for "long horizontal columns and short vertical rows". Thus, a different approach drastically improves performance:
<syntaxhighlight lang=K>prm:{$[x~*x;;:x@o@#x];(x-1){,/'((,(#*x)##x),x)m*(!l)+&\m:~=l:1+#x}/0}
perm:{x[prm[#x]]
perm[" "\"some random text"]
(("text";"text";"random";"some";"random";"some")
("random";"some";"text";"text";"some";"random")
("some";"random";"some";"random";"text";"text"))</syntaxhighlight>
=={{header|Kotlin}}==
Translation of C# recursive 'insert' solution in Wikipedia article on Permutations:
<
fun <T> permute(input: List<T>): List<List<T>> {
Line 4,578 ⟶ 5,515:
println("There are ${perms.size} permutations of $input, namely:\n")
for (perm in perms) println(perm)
}</
{{out}}
Line 4,608 ⟶ 5,545:
[d, c, a, b]
[d, c, b, a]
</pre>
=== Using rotate ===
<syntaxhighlight lang="kotlin">
fun <T> List<T>.rotateLeft(n: Int) = drop(n) + take(n)
fun <T> permute(input: List<T>): List<List<T>> =
when (input.isEmpty()) {
true -> listOf(input)
else -> {
permute(input.drop(1))
.map { it + input.first() }
.flatMap { subPerm -> List(subPerm.size) { i -> subPerm.rotateLeft(i) } }
}
}
fun main(args: Array<String>) {
permute(listOf(1, 2, 3)).also {
println("""There are ${it.size} permutations:
|${it.joinToString(separator = "\n")}""".trimMargin())
}
}
</syntaxhighlight>
{{out}}
<pre>
There are 6 permutations:
[3, 2, 1]
[2, 1, 3]
[1, 3, 2]
[2, 3, 1]
[3, 1, 2]
[1, 2, 3]
</pre>
=={{header|Lambdatalk}}==
<
{def inject
{lambda {:x :a}
Line 4,638 ⟶ 5,610:
->
[[1,2,3,4],[2,1,3,4],[2,3,1,4],[2,3,4,1],[1,3,2,4],[3,1,2,4],[3,2,1,4],[3,2,4,1],[1,3,4,2],[3,1,4,2],[3,4,1,2],[3,4,2,1],[1,2,4,3],[2,1,4,3],[2,4,1,3],[2,4,3,1],[1,4,2,3],[4,1,2,3],[4,2,1,3],[4,2,3,1],[1,4,3,2],[4,1,3,2],[4,3,1,2],[4,3,2,1]]
</syntaxhighlight>
And this is an illustration of the way lambdatalk builds an interface for javascript functions (the first one is given in this page):
<
1) permutations on sentences
Line 4,713 ⟶ 5,685:
321
</syntaxhighlight>
=={{header|langur}}==
Line 4,719 ⟶ 5,691:
This follows the Go language non-recursive example, but is not limited to integers, or even to numbers.
<syntaxhighlight lang="langur">val .factorial = fn .x: if(.x < 2: 1; .x * self(.x - 1))
val .permute = fn(.list) {
if .list is not list: throw "expected list"
val .limit = 10
if len(.
var .elements = .
var .ordinals = pseries len .elements
Line 4,736 ⟶ 5,705:
var .i, .j
for[.p=[.
.i = .n - 1
.j = .n
Line 4,760 ⟶ 5,729:
for .e in .permute([1, 3.14, 7]) {
writeln .e
}
</syntaxhighlight>
{{out}}
Line 4,772 ⟶ 5,742:
=={{header|LFE}}==
<
(defun permute
(('())
Line 4,780 ⟶ 5,750:
(<- y (permute (-- l `(,x)))))
(cons x y))))
</syntaxhighlight>
REPL usage:
<
> (permute '(1 2 3))
((1 2 3) (1 3 2) (2 1 3) (2 3 1) (3 1 2) (3 2 1))
</syntaxhighlight>
=={{header|Lobster}}==
<syntaxhighlight lang="lobster">
// Lobster implementation of the (very fast) Go example
// http://rosettacode.org/wiki/Permutations#Go
Line 4,998 ⟶ 5,891:
permi(se): print(_)
</syntaxhighlight>
{{out}}
<pre>
Line 5,104 ⟶ 5,997:
=={{header|Logtalk}}==
<
:- public(permutation/2).
Line 5,125 ⟶ 6,018:
select(Head, Tail, Tail2).
:- end_object.</
{{out|Usage example}}
<
[1,2,3]
Line 5,135 ⟶ 6,028:
[3,1,2]
[3,2,1]
yes</
=={{header|Lua}}==
<
local function permutation(a, n, cb)
if n == 0 then
Line 5,157 ⟶ 6,050:
end
permutation({1,2,3}, 3, callback)
</syntaxhighlight>
{{out}}
<pre>
Line 5,168 ⟶ 6,061:
</pre>
<
-- Iterative version
Line 5,201 ⟶ 6,094:
ipermutations(3, 3)
</syntaxhighlight>
<pre>
Line 5,213 ⟶ 6,106:
=== fast, iterative with coroutine to use as a generator ===
<
#!/usr/bin/env luajit
-- Iterative version
Line 5,255 ⟶ 6,148:
print(table.concat(p, " "))
end
</syntaxhighlight>
{{out}}
Line 5,270 ⟶ 6,163:
=={{header|M2000 Interpreter}}==
===All permutations in one module===
<syntaxhighlight lang="m2000 interpreter">
Module Checkit {
Global a$
Line 5,315 ⟶ 6,208:
}
Checkit
</syntaxhighlight>
===Step by step Generator===
<syntaxhighlight lang="m2000 interpreter">
Module StepByStep {
Function PermutationStep (a) {
Line 5,362 ⟶ 6,255:
StepByStep
</syntaxhighlight>
{{out}}
<pre style="height:30ex;overflow:scroll">
Line 5,432 ⟶ 6,325:
A peculiarity of this implementation is my use of arithmetic rather than branching to compute Sedgewick’s ‘k’. (I use arithmetic similarly in my Ratfor 77 implementation.)
<
# 1-based indexing of a string's characters.
Line 5,466 ⟶ 6,359:
divert`'dnl
permutations(`123')
permutations(`abcd')</
{{out}}
Line 5,504 ⟶ 6,397:
=={{header|Maple}}==
<
[[1, 2, 3], [1, 3, 2], [2, 1, 3], [2, 3, 1], [3, 1, 2], [3, 2, 1]]
combinat:-permute([a,b,c]);
[[a, b, c], [a, c, b], [b, a, c], [b, c, a], [c, a, b], [c, b, a]]</
An implementation based on Mathematica solution:
<
insert:=(v,a,n)->`if`(n>nops(v),[op(v),a],subsop(n=(a,v[n]),v)):
perm:=s->fold((a,b)->map(u->seq(insert(u,b,k+1),k=0..nops(u)),a),[[]],s):
perm([$1..3]);
[[3, 2, 1], [2, 3, 1], [2, 1, 3], [3, 1, 2], [1, 3, 2], [1, 2, 3]]</
=={{header|Mathematica}}/{{header|Wolfram Language}}==
Line 5,523 ⟶ 6,416:
===Version from scratch===
<syntaxhighlight lang="mathematica">
(***Standard list functions:*)
fold[f_, x_, {}] := x
Line 5,535 ⟶ 6,428:
Table[insert[L, #2, k + 1], {k, 0, Length[L]}]] /@ #1) &, {{}},
S]
</syntaxhighlight>
{{out}}
Line 5,546 ⟶ 6,439:
===Built-in version===
<
{{out}}
<pre>{{1, 2, 3, 4}, {1, 2, 4, 3}, {1, 3, 2, 4}, {1, 3, 4, 2}, {1, 4, 2, 3}, {1, 4, 3, 2}, {2, 1, 3, 4}, {2, 1, 4, 3}, {2, 3, 1, 4}, {2, 3,
Line 5,553 ⟶ 6,446:
=={{header|MATLAB}} / {{header|Octave}}==
<
{{out}}
<pre>4321
Line 5,581 ⟶ 6,474:
=={{header|Maxima}}==
<
n: length(v), i: 0,
for k: n - 1 thru 1 step -1 do (if v[k] < v[k + 1] then (i: k, return())),
Line 5,604 ⟶ 6,497:
[2, 3, 1]
[3, 1, 2]
[3, 2, 1] */</
===Builtin version===
<
(%i1) permutations([1, 2, 3]);
(%o1) {[1, 2, 3], [1, 3, 2], [2, 1, 3], [2, 3, 1], [3, 1, 2], [3, 2, 1]}
</syntaxhighlight>
=={{header|Mercury}}==
<
:- module permutations2.
:- interface.
Line 5,651 ⟶ 6,544:
nl(!IO),
print(all_permutations2([1,2,3,4]),!IO).
</syntaxhighlight>
{{out}}
Line 5,658 ⟶ 6,551:
sol([[1, 2, 3, 4], [1, 2, 4, 3], [1, 3, 2, 4], [1, 3, 4, 2], [1, 4, 2, 3], [1, 4, 3, 2], [2, 1, 3, 4], [2, 1, 4, 3], [2, 3, 1, 4], [2, 3, 4, 1], [2, 4, 1, 3], [2, 4, 3, 1], [3, 1, 2, 4], [3, 1, 4, 2], [3, 2, 1, 4], [3, 2, 4, 1], [3, 4, 1, 2], [3, 4, 2, 1], [4, 1, 2, 3], [4, 1, 3, 2], [4, 2, 1, 3], [4, 2, 3, 1], [4, 3, 1, 2], [4, 3, 2, 1]])
sol([[1, 2, 3, 4], [1, 2, 4, 3], [1, 3, 2, 4], [1, 3, 4, 2], [1, 4, 2, 3], [1, 4, 3, 2], [2, 1, 3, 4], [2, 1, 4, 3], [2, 3, 1, 4], [2, 3, 4, 1], [2, 4, 1, 3], [2, 4, 3, 1], [3, 1, 2, 4], [3, 1, 4, 2], [3, 2, 1, 4], [3, 2, 4, 1], [3, 4, 1, 2], [3, 4, 2, 1], [4, 1, 2, 3], [4, 1, 3, 2], [4, 2, 1, 3], [4, 2, 3, 1], [4, 3, 1, 2], [4, 3, 2, 1]])
</pre>
=={{header|Modula-2}}==
{{works with|ADW Modula-2 (1.6.291)}}
<
FROM Terminal
Line 5,797 ⟶ 6,614:
IF n > 0 THEN permute(n) END;
(*Wait*)
END Permute.</
=={{header|Modula-3}}==
Line 5,804 ⟶ 6,621:
This implementation merely prints out the orbit of the list (1, 2, ..., n) under the action of <i>S<sub>n</sub></i>. It shows off Modula-3's built-in <code>Set</code> type and uses the standard <code>IntSeq</code> library module.
<
IMPORT IO, IntSeq;
Line 5,861 ⟶ 6,678:
GeneratePermutations(chosen, values);
END Permutations.</
{{out}}
Line 5,882 ⟶ 6,699:
Suppose that <code>D</code> is the domain of elements to be permuted. This module requires a <code>DomainSeq</code> (<code>Sequence</code> of <code>D</code>), a <code>DomainSet</code> (<code>Set</code> of <code>D</code>), and a <code>DomainSeqSeq</code> (<code>Sequence</code> of <code>Sequence</code>s of <code>Domain</code>).
<
(*
Line 5,909 ⟶ 6,726:
*)
END GenericPermutations.</
;implementation
Line 5,915 ⟶ 6,732:
In addition to the interface's specifications, this requires a generic <code>Domain</code>. Some implementations of a set are not safe to iterate over while modifying (e.g., a tree), so this copies the values and iterates over them.
<
(*
Line 5,985 ⟶ 6,802:
BEGIN
END GenericPermutations.</
;Sample Usage
Line 5,991 ⟶ 6,808:
Here the domain is <code>Integer</code>, but the interface doesn't require that, so we "merely" need <code>IntSeq</code> (a <code>Sequence</code> of <code>Integer</code>), <code>IntSetTree</code> (a set type I use, but you could use <code>SetDef</code> or <code>SetList</code> if you prefer; I've tested it and it works), <code>IntSeqSeq</code> (a <code>Sequence</code> of <code>Sequence</code>s of <code>Integer</code>), and <code>IntPermutations</code>, which is <code>GenericPermutations</code> instantiated for <code>Integer</code>.
<
IMPORT IO, IntSeq, IntSetTree, IntSeqSeq, IntPermutations;
Line 6,033 ⟶ 6,850:
END;
END GPermutations.</
{{out}} (somewhat edited!)
Line 6,047 ⟶ 6,864:
=={{header|NetRexx}}==
<
options replace format comments java crossref symbols nobinary
Line 6,195 ⟶ 7,012:
end thing
return
</syntaxhighlight>
{{out}}
<pre style="height:55ex;overflow:scroll">
Line 6,243 ⟶ 7,060:
===Using the standard library===
<
var v = [1, 2, 3] # List has to start sorted
echo v
while v.nextPermutation():
echo v</
{{out}}
Line 6,258 ⟶ 7,075:
[3, 2, 1]
</pre>
===Single yield iterator===
<syntaxhighlight lang="nim">
iterator inplacePermutations[T](xs: var seq[T]): var seq[T] =
assert xs.len <= 24, "permutation of array longer than 24 is not supported"
let n = xs.len - 1
var
c: array[24, int8]
i: int = 0
for i in 0 .. n: c[i] = int8(i+1)
while true:
yield xs
if i >= n: break
c[i] -= 1
let j = if (i and 1) == 1: 0 else: int(c[i])
swap(xs[i+1], xs[j])
i = 0
while c[i] == 0:
let t = i+1
c[i] = int8(t)
i = t
</syntaxhighlight>
verification
<syntaxhighlight lang="nim">
import intsets
from math import fac
block:
# test all permutations of length from 0 to 9
for l in 0..9:
# prepare data
var xs = newSeq[int](l)
for i in 0..<l: xs[i] = i
var s = initIntSet()
for cs in inplacePermutations(xs):
# each permutation must be of length l
assert len(cs) == l
# each permutation must contain digits from 0 to l-1 exactly once
var ds = newSeq[bool](l)
for c in cs:
assert not ds[c]
ds[c] = true
# generate a unique number for each permutation
var h = 0
for e in cs:
h = l * h + e
assert not s.contains(h)
s.incl(h)
# check exactly l! unique number of permutations
assert len(s) == fac(l)
</syntaxhighlight>
===Translation of C===
{{trans|C}}
<
iterator permutations[T](ys: openarray[T]): seq[T] =
var
Line 6,279 ⟶ 7,157:
inc d
if d >= ys.len: break outer
let i = if (d and 1) == 1: c[d] else: 0
swap xs[i], xs[d]
Line 6,288 ⟶ 7,165:
for i in permutations(x):
echo i</
Output:
<pre>@[1, 2, 3]
Line 6,299 ⟶ 7,176:
===Translation of Go===
{{trans|Go}}
<
# http://rosettacode.org/wiki/Permutations#Go
# implementing a recursive https://en.wikipedia.org/wiki/Steinhaus–Johnson–Trotter_algorithm
Line 6,331 ⟶ 7,208:
var se = @[0, 1, 2, 3] #, 4, 5, 6, 7, 8, 9, 10]
perm(se, proc(s: openArray[int])= echo s)</
=={{header|OCaml}}==
<
Translation of Ada version. *)
let next_perm p =
Line 6,378 ⟶ 7,255:
2 3 1
3 1 2
3 2 1 *)</
Permutations can also be defined on lists recursively:
<
let n = List.length l in
if n = 1 then [l] else
Line 6,394 ⟶ 7,271:
let print l = List.iter (Printf.printf " %d") l; print_newline() in
List.iter print (permutations [1;2;3;4])</
or permutations indexed independently:
<
let a, b = let c = k/n in c, k-(n*c) in
let e = List.nth l b in
Line 6,412 ⟶ 7,289:
done
let () = show_perms [1;2;3;4]</
=={{header|ooRexx}}==
Essentially derived fom the program shown under rexx.
This program works also with Regina (and other REXX implementations?)
<
/* REXX Compute bunch permutations of things elements */
Parse Arg bunch things
Line 6,503 ⟶ 7,380:
Say 'rexx perm 2 4 -> Permutations of 1 2 3 4 in 2 positions'
Say 'rexx perm 2 a b c d -> Permutations of a b c d in 2 positions'
Exit</
{{out}}
<pre>H:\>rexx perm 2 U V W X
Line 6,528 ⟶ 7,405:
=={{header|OpenEdge/Progress}}==
<syntaxhighlight lang="openedge/progress">
DEFINE VARIABLE charArray AS CHARACTER EXTENT 3 INITIAL ["A","B","C"].
DEFINE VARIABLE sizeofArray AS INTEGER.
Line 6,563 ⟶ 7,440:
charArray[a] = charArray[b].
charArray[b] = temp.
END PROCEDURE. </
{{out}}
<pre>ABC
Line 6,573 ⟶ 7,450:
=={{header|PARI/GP}}==
<
=={{header|Pascal}}==
<
var
Line 6,646 ⟶ 7,523:
next;
until is_last;
end.</
===alternative===
a little bit more speed.I take n = 12.
Line 6,652 ⟶ 7,529:
But you have to use the integers [1..n] directly or as Index to your data.
1 to n are in lexicographic order.
<
{$MODE DELPHI}
{$ELSE}
Line 6,722 ⟶ 7,599:
writeln(permcnt);
writeln(FormatDateTime('HH:NN:SS.zzz',T1-T0));
end.</
{{Out}}
{fpc 2.64/3.0 32Bit or 3.1 64 Bit i4330 3.5 Ghz same timings.
Line 6,729 ⟶ 7,606:
479001600 //= 12!
00:00:01.328</pre>
===Permutations from integers===
A console application in Free Pascal, created with the Lazarus IDE.
<syntaxhighlight lang="pascal">
program Permutations;
(*
Demonstrates four closely related ways of establishing a bijection between
permutations of 0..(n-1) and integers 0..(n! - 1).
Each integer in that range is represented by mixed-base digits d[0..n-1],
where each d[j] satisfies 0 <= d[j] <=j.
The integer represented by d[0..n-1] is
d[n-1]*(n-1)! + d[n-2]*(n-2)! + ... + d[1]*1! + d[0]*0!
where the last term can be omitted in practice because d[0] is always 0.
See the section "Numbering permutations" in the Wikipedia article
"Permutation" (NB their digit array d is 1-based).
*)
uses SysUtils, TypInfo;
type TPermIntMapping = (map_I, map_J, map_K, map_L);
type TPermutation = array of integer;
// Function to map an integer to a permutation.
function IntToPerm( map : TPermIntMapping;
nrItems, z : integer) : TPermutation;
var
d, lookup : array of integer;
x, y : integer;
h, j, k, m : integer;
begin
SetLength( result, nrItems);
SetLength( lookup, nrItems);
SetLength( d, nrItems);
m := nrItems - 1;
// Convert z to digits d[0..m] (see comment at head of program).
d[0] := 0;
y := z;
for j := 1 to m - 1 do begin
x := y div (j + 1);
d[j] := y - x*(j + 1);
y := x;
end;
d[m] := y;
// Set up the permutation elements
case map of
map_I, map_L: for j := 0 to m do lookup[j] := j;
map_J, map_K: for j := 0 to m do lookup[j] := m - j;
end;
for j := m downto 0 do begin
k := d[j];
case map of
map_I: result[lookup[k]] := m - j;
map_J: result[j] := lookup[k];
map_K: result[lookup[k]] := j;
map_L: result[m - j] := lookup[k];
end;
// When lookup[k] has been used, it's removed from the lookup table
// and the elements above it are moved down one place.
for h := k to j - 1 do lookup[h] := lookup[h + 1];
end;
end;
// Function to map a permutation to an integer; inverse of the above.
// Put in for completeness, not required for Rosetta Code task.
function PermToInt( map : TPermIntMapping;
p : TPermutation) : integer;
var
m, i, j, k : integer;
d : array of integer;
begin
m := High(p); // number of items in permutation is m + 1
SetLength( d, m + 1);
for k := 0 to m do d[k] := 0; // initialize all digits to 0
// Looking for inversions
for i := 0 to m - 1 do begin
for j := i + 1 to m do begin
if p[j] < p[i] then begin
case map of
map_I : inc( d[m - p[j]]);
map_J : inc( d[j]);
map_K : inc( d[p[i]]);
map_L : inc( d[m - i]);
end;
end;
end;
end;
// Get result from its digits (see comment at head of program).
result := d[m];
for j := m downto 2 do result := result*j + d[j - 1];
end;
// Main routine to generate permutations of the integers 0..(n-1),
// where n is passed as a command-line parameter, e.g. Permutations 4
var
n, n_fac, z, j : integer;
nrErrors : integer;
perm : TPermutation;
map : TPermIntMapping;
lineOut : string;
pinfo : TypInfo.PTypeInfo;
begin
n := SysUtils.StrToInt( ParamStr(1));
n_fac := 1;
for j := 2 to n do n_fac := n_fac*j;
pinfo := System.TypeInfo( TPermIntMapping);
lineOut := 'integer';
for map := Low( TPermIntMapping) to High( TPermIntMapping) do begin
lineOut := lineOut + ' ' + TypInfo.GetEnumName( pinfo, ord(map));
end;
WriteLn( lineOut);
for z := 0 to n_fac - 1 do begin
lineOut := SysUtils.Format( '%7d', [z]);
for map := Low( TPermIntMapping) to High( TPermIntMapping) do begin
perm := IntToPerm( map, n, z);
// Check the inverse mapping (not required for Rosetta Code task)
Assert( z = PermToInt( map, perm));
lineOut := lineOut + ' ';
for j := 0 to n - 1 do
lineOut := lineOut + SysUtils.Format( '%d', [perm[j]]);
end;
WriteLn( lineOut);
end;
end.
</syntaxhighlight>
{{out}}
<pre>
integer map_I map_J map_K map_L
0 0123 0123 0123 0123
1 0132 1023 1023 0132
2 0213 0213 0213 0213
3 0312 2013 1203 0231
4 0231 1203 2013 0312
5 0321 2103 2103 0321
6 1023 0132 0132 1023
7 1032 1032 1032 1032
8 2013 0312 0231 1203
9 3012 3012 1230 1230
10 2031 1302 2031 1302
11 3021 3102 2130 1320
12 1203 0231 0312 2013
13 1302 2031 1302 2031
14 2103 0321 0321 2103
15 3102 3021 1320 2130
16 2301 2301 2301 2301
17 3201 3201 2310 2310
18 1230 1230 3012 3012
19 1320 2130 3102 3021
20 2130 1320 3021 3102
21 3120 3120 3120 3120
22 2310 2310 3201 3201
23 3210 3210 3210 3210
</pre>
=={{header|Perl}}==
A simple recursive implementation.
<
my ($perm,@set) = @_;
print "$perm\n" || return unless (@set);
Line 6,738 ⟶ 7,766:
}
my @input = (qw/a b c d/);
permutation('',@input);</
{{out}}
<pre>abcd
Line 6,767 ⟶ 7,795:
For better performance, use a module like <code>ntheory</code> or <code>Algorithm::Permute</code>.
{{libheader|ntheory}}
<
my @tasks = (qw/party sleep study/);
forperm {
print "@tasks[@_]\n";
} @tasks;</
{{out}}
<pre>
Line 6,783 ⟶ 7,811:
=={{header|Phix}}==
<!--<
<span style="color: #008080;">with</span> <span style="color: #008080;">javascript_semantics</span>
<span style="color: #7060A8;">requires</span><span style="color: #0000FF;">(</span><span style="color: #008000;">"1.0.2"</span><span style="color: #0000FF;">)</span>
<span style="color: #0000FF;">?</span><span style="color: #7060A8;">shorten</span><span style="color: #0000FF;">(</span><span style="color: #7060A8;">permutes</span><span style="color: #0000FF;">(</span><span style="color: #008000;">"abcd"</span><span style="color: #0000FF;">),</span><span style="color: #008000;">"elements"</span><span style="color: #0000FF;">,</span><span style="color: #000000;">5</span><span style="color: #0000FF;">)</span>
<!--</
{{out}}
<pre>
Line 6,795 ⟶ 7,823:
=={{header|Phixmonti}}==
<
def save
Line 6,818 ⟶ 7,846:
( ) >ps
( ) ( 1 2 3 4 ) permute
ps> sort print</
=={{header|Picat}}==
Picat has built-in support for permutations:
* <code>permutation(L)</code>: Generates all permutations for a list L.
* <code>permutation(L,P)</code>: Generates (via backtracking) all permutations for a list L.
===Recursion===
Use <code>findall/2</code> to find all permutations. See example below.
<syntaxhighlight lang="picat">permutation_rec1([X|Y],Z) :-
permutation_rec1(Y,W),
select(X,Z,W).
permutation_rec1([],[]).
permutation_rec2([], []).
permutation_rec2([X], [X]) :-!.
permutation_rec2([T|H], X) :-
permutation_rec2(H, H1),
append(L1, L2, H1),
append(L1, [T], X1),
append(X1, L2, X).</syntaxhighlight>
===Constraint modelling===
Constraint modelling only handles integers, and here generates all permutations of a list 1..N for a given N.
<code>permutation_cp_list(L)</code> permutes a list via <code>permutation_cp2/1</code>.
<syntaxhighlight lang="picat">import cp.
% Returns all permutations
permutation_cp1(N) = solve_all(X) =>
X = new_list(N),
X :: 1..N,
all_different(X).
% Find next permutation on backtracking
permutation_cp2(N,X) =>
X = new_list(N),
X :: 1..N,
all_different(X),
solve(X).
% Use the cp approach on a list L.
permutation_cp_list(L) = Perms =>
Perms = [ [L[I] : I in P] : P in permutation_cp1(L.len)].</syntaxhighlight>
===Tests===
Here is a test of the different approaches, including the two built-ins.
<syntaxhighlight lang="picat">import util, cp.
main =>
N = 3,
println(permutations=permutations(1..N)), % built in
println(permutation=findall(P,permutation([a,b,c],P))), % built-in
println(permutation_rec1=findall(P,permutation_rec1(1..N,P))),
println(permutation_rec2=findall(P,permutation_rec2(1..N,P))),
println(permutation_cp1=permutation_cp1(N)),
println(permutation_cp2=findall(P,permutation_cp2(N,P))),
println(permutation_cp_list=permutation_cp_list("abc")).</syntaxhighlight>
{{out}}
<pre>permutations = [[1,2,3],[2,1,3],[2,3,1],[1,3,2],[3,1,2],[3,2,1]]
permutation = [abc,acb,bac,bca,cab,cba]
permutation_rec1 = [[1,2,3],[2,1,3],[2,3,1],[1,3,2],[3,1,2],[3,2,1]]
permutation_rec2 = [[1,2,3],[2,1,3],[2,3,1],[1,3,2],[3,1,2],[3,2,1]]
permutation_cp1 = [[1,2,3],[1,3,2],[2,1,3],[2,3,1],[3,1,2],[3,2,1]]
permutation_cp2 = [[1,2,3],[1,3,2],[2,1,3],[2,3,1],[3,1,2],[3,2,1]]
permutation_cp_list = [abc,acb,bac,bca,cab,cba]</pre>
=={{header|PicoLisp}}==
<
(permute (1 2 3))</
{{out}}
<pre>-> ((1 2 3) (1 3 2) (2 1 3) (2 3 1) (3 1 2) (3 2 1))</pre>
=={{header|PowerShell}}==
<syntaxhighlight lang="powershell">
function permutation ($array) {
function generate($n, $array, $A) {
Line 6,903 ⟶ 7,949:
}
permutation @('A','B','C')
</syntaxhighlight>
<b>Output:</b>
<pre>
Line 6,916 ⟶ 7,962:
=={{header|Prolog}}==
Works with SWI-Prolog and library clpfd,
<
permut_clpfd(L, N) :-
Line 6,922 ⟶ 7,968:
L ins 1..N,
all_different(L),
label(L).</
{{out}}
<
[1,2,3]
[1,3,2]
Line 6,932 ⟶ 7,978:
[3,2,1]
false.
</syntaxhighlight>
A declarative way of fetching permutations:
<
% P is a permutation of L
Line 6,940 ⟶ 7,986:
permut_Prolog([H | T], NL) :-
select(H, NL, NL1),
permut_Prolog(T, NL1).</
{{out}}
<
[ab,cd,ef]
[ab,ef,cd]
Line 6,949 ⟶ 7,995:
[ef,ab,cd]
[ef,cd,ab]
false.</
{{Trans|Curry}}
<syntaxhighlight lang="prolog">
insert(X, L, [X|L]).
insert(X, [Y|Ys], [Y|L2]) :- insert(X, Ys, L2).
Line 6,957 ⟶ 8,003:
permutation([], []).
permutation([X|Xs], P) :- permutation(Xs, L), insert(X, L, P).
</syntaxhighlight>
{{Out}}
<pre>
Line 6,969 ⟶ 8,015:
false.
</pre>
=={{header|Python}}==
Line 7,043 ⟶ 8,020:
===Standard library function===
{{works with|Python|2.6+}}
<
for values in itertools.permutations([1,2,3]):
print (values)</
{{out}}
<pre>
Line 7,060 ⟶ 8,037:
The follwing functions start from a list [0 ... n-1] and exchange elements to always have a valid permutation. This is done recursively: first exchange a[0] with all the other elements, then a[1] with a[2] ... a[n-1], etc. thus yielding all permutations.
<
a = list(range(n))
def sub(i):
Line 7,085 ⟶ 8,062:
a[k - 1] = a[k]
a[n - 1] = x
yield from sub(0)</
These two solutions make use of a generator, and "yield from" introduced in [https://www.python.org/dev/peps/pep-0380/ PEP-380]. They are slightly different: the latter produces permutations in lexicographic order, because the "remaining" part of a (that is, a[i+1:]) is always sorted, whereas the former always reverses the exchange just after the recursive call.
Line 7,091 ⟶ 8,068:
On three elements, the difference can be seen on the last two permutations:
<
(0, 1, 2)
(0, 2, 1)
Line 7,105 ⟶ 8,082:
(1, 2, 0)
(2, 0, 1)
(2, 1, 0)</
=== Iterative implementation ===
Line 7,111 ⟶ 8,088:
Given a permutation, one can easily compute the ''next'' permutation in some order, for example lexicographic order, here. Then to get all permutations, it's enough to start from [0, 1, ... n-1], and store the next permutation until [n-1, n-2, ... 0], which is the last in lexicographic order.
<
n = len(a)
i = n - 1
Line 7,149 ⟶ 8,126:
(1, 2, 0)
(2, 0, 1)
(2, 1, 0)</
=== Implementation using destructive list updates ===
<
def permutations(xs):
ac = [[]]
Line 7,166 ⟶ 8,143:
print(permutations([1,2,3,4]))
</syntaxhighlight>
===Functional :: type-preserving===
Line 7,174 ⟶ 8,151:
{{Works with|Python|3.7}}
<
from functools import (reduce)
Line 7,259 ⟶ 8,236:
# MAIN ---
if __name__ == '__main__':
main()</
{{Out}}
<pre>[1, 2, 3] -> [[1,2,3],[2,3,1],[3,1,2],[2,1,3],[1,3,2],[3,2,1]]
Line 7,267 ⟶ 8,244:
=={{header|Qi}}==
{{trans|Erlang}}
<syntaxhighlight lang="qi">
(define insert
L 0 E -> [E|L]
Line 7,286 ⟶ 8,263:
(insert P N H))
(seq 0 (length P))))
(permute T))))</
=={{header|Quackery}}==
===General Solution===
The word ''perms'' solves a more general task; generate permutations of between ''a'' and ''b'' items (inclusive) from the specified nest.
<
[ stack ] is perms.max ( --> [ )
Line 7,324 ⟶ 8,302:
' [ 1 2 3 ] permutations echo cr
$ "quack" permutations 60 wrap$
$ "quack" 3 4 perms 46 wrap$</
'''Output:'''
Line 7,361 ⟶ 8,339:
kucq kuca kaq kaqu kaqc kau kauq kauc kac kacq
kacu kcq kcqu kcqa kcu kcuq kcua kca kcaq kcau</pre>
===An Uncommon Ordering===
Edit: I ''think'' this process is called "iterative deepening". Would love to have this confirmed or corrected.
The central idea is that given a list of the permutations of say 3 items, each permutation can be used to generate 4 of the permutations of 4 items, so for example, from <code>[ 3 1 2 ]</code> we can generate
::<code>[ 0 3 1 2 ]</code>
::<code>[ 3 0 1 2 ]</code>
::<code>[ 3 1 0 2 ]</code>
::<code>[ 3 1 2 0 ]</code>
by stuffing the 0 into each of the 4 possible positions that it could go.
The code start with a nest of all the permutations of 0 items <code>[ [ ] ]</code>, and each time though the outer <code>times</code> loop (i.e. 4 times in the example) it takes each of the permutations generated so far (this is the <code>witheach</code> loop) and applies the central idea described above (that is the inner <code>times</code> loop.)
'''Some aids to reading the code.'''
Quackery is a stack based language. If you are unfamiliar the with words <code>swap</code>, <code>rot</code>, <code>dup</code>, <code>2dup</code>, <code>dip</code>, <code>unrot</code> or <code>drop</code> they can be skimmed over as "noise" to get a gist of the process.
<code>[]</code> creates an empty nest <code>[ ]</code>.
<code>times</code> indicates that the word or nest following it is to be repeated a specified number of times. (The specified number is on the top of the stack, so <code>4 times [ ... ]</code>repeats some arbitrary code 4 times.)
<code>i</code> returns the number of times a <code>times</code> loop has left to repeat. It counts down to zero.
<code>i^</code> returns the number of times a <code>times</code> loop has been repeated. It counts up from zero.
<code>size</code> returns the number of items (words, numbers, nests) in a nest.
<code>witheach</code> indicates that the word or nest following it is to be repeated once for each item in a specified nest, with successive items from the nest available on the top of stack on each repetition.
<code>999 ' [ 10 11 12 13 ] 3 stuff</code> will return <code>[ 10 11 12 999 13 ]</code>by stuffing the number 999 into the 3rd position in the nest. (The start of a nest is the zeroth position, the end of this nest is the 5th position.)
<code>nested join</code> adds a nest to the end of a nest as its last item.
<syntaxhighlight lang="quackery"> [ ' [ [ ] ] swap times
[ [] i rot witheach
[ dup size 1+ times
[ 2dup i^ stuff
dip rot nested join
unrot ] drop ] drop ] ] is perms ( n --> [ )
4 perms witheach [ echo cr ]</syntaxhighlight>
{{out}}
<pre>[ 0 1 2 3 ]
[ 1 0 2 3 ]
[ 1 2 0 3 ]
[ 1 2 3 0 ]
[ 0 2 1 3 ]
[ 2 0 1 3 ]
[ 2 1 0 3 ]
[ 2 1 3 0 ]
[ 0 2 3 1 ]
[ 2 0 3 1 ]
[ 2 3 0 1 ]
[ 2 3 1 0 ]
[ 0 1 3 2 ]
[ 1 0 3 2 ]
[ 1 3 0 2 ]
[ 1 3 2 0 ]
[ 0 3 1 2 ]
[ 3 0 1 2 ]
[ 3 1 0 2 ]
[ 3 1 2 0 ]
[ 0 3 2 1 ]
[ 3 0 2 1 ]
[ 3 2 0 1 ]
[ 3 2 1 0 ]
</pre>
=={{header|R}}==
===Iterative version===
<
n <- length(a)
i <- n
Line 7,398 ⟶ 8,446:
}
unname(e)
}</
'''Example'''
<syntaxhighlight lang="text">> perm(3)
[,1] [,2] [,3] [,4] [,5] [,6]
[1,] 1 1 2 2 3 3
[2,] 2 3 1 3 1 2
[3,] 3 2 3 1 2 1</
===Recursive version===
<
linsert <- function(x,s) lapply(0:length(s), function(k) append(s,x,k))
Line 7,420 ⟶ 8,468:
# permutations of a vector s
permutation <- function(s) lapply(perm(length(s)), function(i) s[i])
</syntaxhighlight>
Output:
<
[[1]]
[1] "c" "b" "a"
Line 7,440 ⟶ 8,488:
[[6]]
[1] "a" "b" "c"</
=={{header|Racket}}==
<
#lang racket
Line 7,504 ⟶ 8,552:
(next-perm (permuter))))))
;; -> (A B C)(A C B)(B A C)(B C A)(C A B)(C B A)
</syntaxhighlight>
=={{header|Raku}}==
Line 7,510 ⟶ 8,558:
{{works with|rakudo|2018.10}}
First, you can just use the built-in method on any list type.
<syntaxhighlight lang="raku"
{{out}}
<pre>a b c
Line 7,520 ⟶ 8,568:
Here is some generic code that works with any ordered type. To force lexicographic ordering, change <tt>after</tt> to <tt>gt</tt>. To force numeric order, replace it with <tt>></tt>.
<syntaxhighlight lang="raku"
my $j = @a.end - 1;
return Nil if --$j < 0 while @a[$j] after @a[$j+1];
Line 7,535 ⟶ 8,583:
}
.say for [<a b c>], &next_perm ...^ !*;</
{{out}}
<pre>a b c
Line 7,545 ⟶ 8,593:
</pre>
Here is another non-recursive implementation, which returns a lazy list. It also works with any type.
<syntaxhighlight lang="raku"
my @seq := 1..+@items;
gather for (^[*] @seq) -> $n is copy {
Line 7,557 ⟶ 8,605:
}
}
.say for permute( 'a'..'c' )</
{{out}}
<pre>(a b c)
Line 7,566 ⟶ 8,614:
(c b a)</pre>
Finally, if you just want zero-based numbers, you can call the built-in function:
<syntaxhighlight lang="raku"
{{out}}
<pre>0 1 2
Line 7,574 ⟶ 8,622:
2 0 1
2 1 0</pre>
=={{Header|RATFOR}}==
For translation to FORTRAN 77 with the public domain ratfor77 preprocessor.
<syntaxhighlight lang="ratfor"># Heap’s algorithm for generating permutations. Algorithm 2 in
# Robert Sedgewick, 1977. Permutation generation methods. ACM
# Comput. Surv. 9, 2 (June 1977), 137-164.
define(n, 3)
define(n_minus_1, 2)
implicit none
integer a(1:n)
integer c(1:n)
integer i, k
integer tmp
10000 format ('(', I1, n_minus_1(' ', I1), ')')
# Initialize the data to be permuted.
do i = 1, n {
a(i) = i
}
# What follows is a non-recursive Heap’s algorithm as presented by
# Sedgewick. Sedgewick neglects to fully initialize c, so I have
# corrected for that. Also I compute k without branching, by instead
# doing a little arithmetic.
do i = 1, n {
c(i) = 1
}
i = 2
write (*, 10000) a
while (i <= n) {
if (c(i) < i) {
k = mod (i, 2) + ((1 - mod (i, 2)) * c(i))
tmp = a(i)
a(i) = a(k)
a(k) = tmp
c(i) = c(i) + 1
i = 2
write (*, 10000) a
} else {
c(i) = 1
i = i + 1
}
}
end</syntaxhighlight>
Here is what the generated FORTRAN 77 code looks like:
<syntaxhighlight lang="fortran">C Output from Public domain Ratfor, version 1.0
implicit none
integer a(1: 3)
integer c(1: 3)
integer i, k
integer tmp
10000 format ('(', i1, 2(' ', i1), ')')
do23000 i = 1, 3
a(i) = i
23000 continue
23001 continue
do23002 i = 1, 3
c(i) = 1
23002 continue
23003 continue
i = 2
write (*, 10000) a
23004 if(i .le. 3)then
if(c(i) .lt. i)then
k = mod (i, 2) + ((1 - mod (i, 2)) * c(i))
tmp = a(i)
a(i) = a(k)
a(k) = tmp
c(i) = c(i) + 1
i = 2
write (*, 10000) a
else
c(i) = 1
i = i + 1
endif
goto 23004
endif
23005 continue
end</syntaxhighlight>
{{out}}
$ ratfor77 permutations.r > permutations.f && f2c permutations.f && cc -o permutations permutations.c -lf2c && ./permutations
<pre>(1 2 3)
(2 1 3)
(3 1 2)
(1 3 2)
(2 3 1)
(3 2 1)</pre>
=={{header|REXX}}==
This program could be simplified quite a bit if the "things" were just restricted to numbers (numerals),
<br>but that would make it specific to numbers and not "things" or objects.
<
parse arg things bunch inbetweenChars names /*obtain optional arguments from the CL*/
if things=='' | things=="," then things= 3 /*Not specified? Then use the default.*/
Line 7,616 ⟶ 8,760:
@.?= $.q; call .permSet ?+1
end /*q*/
return</
{{out|output|text= when the following was used for input: <tt> 3 3 </tt>}}
<pre>
Line 7,682 ⟶ 8,826:
=={{header|Ring}}==
<
load "stdlib.ring"
Line 7,730 ⟶ 8,874:
last -= 1
end
</syntaxhighlight>
Output:
<pre>
Line 7,761 ⟶ 8,905:
=={{header|Ring}}==
<
Another Solution
Line 7,814 ⟶ 8,958:
</syntaxhighlight>
Output:
<pre>
Line 7,852 ⟶ 8,996:
=={{header|Ruby}}==
<
{{out}}
<pre>
[[1, 2, 3], [1, 3, 2], [2, 1, 3], [2, 3, 1], [3, 1, 2], [3, 2, 1]]
</pre>
=={{header|Rust}}==
===Iterative===
Uses Heap's algorithm. An in-place version is possible but is incompatible with <code>Iterator</code>.
<
Permutations { idxs: (0..size).collect(), swaps: vec![0; size], i: 0 }
}
Line 7,946 ⟶ 9,044:
vec![2, 1, 0],
]);
}</
===Recursive===
<
fn permute<T, F: Fn(&[T])>(used: &mut Vec<T>, unused: &mut VecDeque<T>, action: &F) {
Line 7,966 ⟶ 9,064:
let mut queue = (1..4).collect::<VecDeque<_>>();
permute(&mut Vec::new(), &mut queue, &|perm| println!("{:?}", perm));
}</
=={{header|SAS}}==
<!-- oh god this code -->
<
data perm;
n=6;
Line 8,011 ⟶ 9,109:
return;
keep p1-p6;
run;</
=={{header|Scala}}==
There is a built-in function in the Scala collections library, that is part of the language's standard library. The permutation function is available on any sequential collection. It could be used as follows given a list of numbers:
<
{{out}}
Line 8,029 ⟶ 9,127:
The following function returns all the permutations of a list:
<
case Nil => List(Nil)
case xs => {
Line 8,039 ⟶ 9,137:
}
}
}</
If you need the unique permutations, use <code>distinct</code> or <code>toSet</code> on either the result or on the input.
Line 8,045 ⟶ 9,143:
=={{header|Scheme}}==
{{trans|Erlang}}
<
(if (= 0 n)
(cons e l)
Line 8,063 ⟶ 9,161:
(insert p n (car l)))
(seq 0 (length p))))
(permute (cdr l))))))</
{{trans|OCaml}}
<
(define (vector-swap! v i j)
(let ((tmp (vector-ref v i)))
Line 8,125 ⟶ 9,223:
; 1 2 0
; 2 0 1
; 2 1 0</
Completely recursive on lists:
<
(cond ((null? s) '())
((null? (cdr s)) (list s))
Line 8,137 ⟶ 9,235:
(splice (cons m l) (car r) (cdr r))))))))
(display (perm '(1 2 3)))</
=={{header|Seed7}}==
<
const type: permutations is array array integer;
Line 8,176 ⟶ 9,274:
writeln;
end for;
end func;</
{{out}}
<pre>
Line 8,188 ⟶ 9,286:
=={{header|Shen}}==
<syntaxhighlight lang="shen">
(define permute
[] -> []
Line 8,207 ⟶ 9,305:
(permute [a b c d])
</syntaxhighlight>
{{out}}
<pre>
Line 8,213 ⟶ 9,311:
</pre>
For lexical order, make a small change:
<syntaxhighlight lang="shen">
(define permute-helper
_ [] -> []
Done [X|Rest] -> (append (prepend-all X (permute (append Done Rest))) (permute-helper (append Done [X]) Rest))
)
</syntaxhighlight>
=={{header|Sidef}}==
===Built-in===
<
say
}</
===Iterative===
<
var idx = @^n
loop {
callback(
var p = n-1
Line 8,247 ⟶ 9,345:
}
forperm({|*p| say p }, 3)</
===Recursive===
<
set
for i in ^set {
__FUNC__(callback, [
set[
], [perm..., set[i]])
}
Line 8,260 ⟶ 9,358:
}
permutations({|p| say p }, [0,1,2])</
{{out}}
<pre>
Line 8,274 ⟶ 9,372:
{{works with|Squeak}}
{{works with|Pharo}}
<
Transcript show: x printString; cr ].</
{{works with|GNU Smalltalk}}
<
ArrayedCollection extend [
Line 8,305 ⟶ 9,403:
[:g |
c map permuteAndDo: [g yield: (c copyFrom: 1 to: c size)]]]
</syntaxhighlight>
Use example:
<syntaxhighlight lang="smalltalk">
st> 'Abc' permutations contents
('bcA' 'cbA' 'cAb' 'Acb' 'bAc' 'Abc' )
</syntaxhighlight>
=={{header|Standard ML}}==
<syntaxhighlight lang="sml">
fun interleave x [] = [[x]]
| interleave x (y::ys) = (x::y::ys) :: (List.map (fn a => y::a) (interleave x ys))
fun perms [] = [[]]
| perms (x::xs) = List.concat (List.map (interleave x) (perms xs))
</syntaxhighlight>
=={{header|Stata}}==
Line 8,318 ⟶ 9,425:
For instance:
<syntaxhighlight lang
'''Program'''
<
local n=`1'
local r=1
Line 8,362 ⟶ 9,469:
} while (i > 1)
}
end</
=={{header|Swift}}==
<
return heaps(&ar, ar.count)
}
Line 8,379 ⟶ 9,486:
}
perms([1, 2, 3]) // [[1, 2, 3], [2, 1, 3], [3, 1, 2], [1, 3, 2], [2, 3, 1], [3, 2, 1]]</
=={{header|Tailspin}}==
This solution seems to be the same as the Kotlin solution. Permutations flow independently without being collected until the end.
<
templates permutations
when <=1> do [1] !
Line 8,398 ⟶ 9,505:
def alpha: ['ABCD'...];
[ $alpha::length -> permutations -> '$alpha($)...;' ] -> !OUT::write
</syntaxhighlight>
{{out}}
<pre>
Line 8,405 ⟶ 9,512:
If we collect all the permutations of the next size down, we can output permutations in lexical order
<
templates lexicalPermutations
when <=1> do [1] !
Line 8,417 ⟶ 9,524:
def alpha: ['ABCD'...];
[ $alpha::length -> lexicalPermutations -> '$alpha($)...;' ] -> !OUT::write
</syntaxhighlight>
{{out}}
<pre>
Line 8,424 ⟶ 9,531:
That algorithm can also be written from the bottom up to produce an infinite stream of sets of larger and larger permutations, until we stop
<
templates lexicalPermutations2
def N: $;
Line 8,437 ⟶ 9,544:
end lexicalPermutations2
def alpha: ['ABCD'...];
[ $alpha::length -> lexicalPermutations2 -> '$alpha($)...;' ] -> !OUT::write
</syntaxhighlight>
{{out}}
<pre>
Line 8,445 ⟶ 9,553:
The solutions above create a lot of new arrays at various stages. We can also use mutable state and just emit a copy for each generated solution.
<
templates perms
templates findPerms
Line 8,464 ⟶ 9,572:
def alpha: ['ABCD'...];
[4 -> perms -> '$alpha($)...;' ] -> !OUT::write
</syntaxhighlight>
{{out}}
<pre>
Line 8,472 ⟶ 9,580:
=={{header|Tcl}}==
{{tcllib|struct::list}}
<
# Make the sequence of digits to be permuted
Line 8,481 ⟶ 9,589:
struct::list foreachperm p $sequence {
puts $p
}</
Testing with <code>tclsh listPerms.tcl 3</code> produces this output:
<pre>
Line 8,491 ⟶ 9,599:
3 2 1
</pre>
=={{header|UNIX Shell}}==
{{works with|Bourne Again SHell}}
{{works with|Korn Shell}}
Straightforward implementation of Heap's algorithm operating in-place on an array local to the <tt>permute</tt> function.
<syntaxhighlight lang="bash">function permute {
if (( $# == 1 )); then
set -- $(seq $1)
fi
local A=("$@")
permuteAn "$#"
}
function permuteAn {
# print all permutations of first n elements of the array A, with remaining
# elements unchanged.
local -i n=$1 i
shift
if (( n == 1 )); then
printf '%s\n' "${A[*]}"
else
permuteAn $(( n-1 ))
for (( i=0; i<n-1; ++i )); do
local -i k
(( k=n%2 ? 0: i ))
local t=${A[k]}
A[k]=${A[n-1]}
A[n-1]=$t
permuteAn $(( n-1 ))
done
fi
}</syntaxhighlight>
For Zsh the array indices need to be bumped by 1 inside the <tt>permuteAn</tt> function:
{{works with|Z Shell}}
<syntaxhighlight lang="zsh">function permuteAn {
# print all permutations of first n elements of the array A, with remaining
# elements unchanged.
local -i n=$1 i
shift
if (( n == 1 )); then
printf '%s\n' "${A[*]}"
else
permuteAn $(( n-1 ))
for (( i=1; i<n; ++i )); do
local -i k
(( k=n%2 ? 1 : i ))
local t=$A[k]
A[k]=$A[n]
A[n]=$t
permuteAn $(( n-1 ))
done
fi
}</syntaxhighlight>
{{Out}}
Sample run:
<pre>$ permute 4
permute 4
1 2 3 4
2 1 3 4
3 1 2 4
1 3 2 4
2 3 1 4
3 2 1 4
4 2 1 3
2 4 1 3
1 4 2 3
4 1 2 3
2 1 4 3
1 2 4 3
1 3 4 2
3 1 4 2
4 1 3 2
1 4 3 2
3 4 1 2
4 3 1 2
4 3 2 1
3 4 2 1
2 4 3 1
4 2 3 1
3 2 4 1
2 3 4 1</pre>
=={{header|Ursala}}==
In practice there's no need to write this because it's in the standard library.
<
permutations =
Line 8,502 ⟶ 9,696:
~&a, # insert the head at the first position
~&ar&& ~&arh2falrtPXPRD), # if the rest is non-empty, recursively insert at all subsequent positions
~&aNC) # no, return the singleton list of the argument</
test program:
<
test = permutations <1,2,3></
{{out}}
<pre><
Line 8,518 ⟶ 9,712:
=={{header|VBA}}==
{{trans|Pascal}}
<
'Generate, count and print (if printem is not false) all permutations of first n integers
Line 8,599 ⟶ 9,793:
Debug.Print "Number of permutations: "; count
End Sub</
{{out|Sample dialogue}}
<pre>
Line 8,636 ⟶ 9,830:
permute 10,False
Number of permutations: 3628800
</pre>
=={{header|VBScript}}==
A recursive implementation. Arrays can contain anything, I stayed with with simple variables. (Elements could be arrays but then the printing routine should be recursive...)
<syntaxhighlight lang="vb">
'permutation ,recursive
a=array("Hello",1,True,3.141592)
cnt=0
perm a,0
wscript.echo vbcrlf &"Count " & cnt
sub print(a)
s=""
for i=0 to ubound(a):
s=s &" " & a(i):
next:
wscript.echo s :
cnt=cnt+1 :
end sub
sub swap(a,b) t=a: a=b :b=t: end sub
sub perm(byval a,i)
if i=ubound(a) then print a: exit sub
for j= i to ubound(a)
swap a(i),a(j)
perm a,i+1
swap a(i),a(j)
next
end sub
</syntaxhighlight>
Output
<pre>
Hello 1 Verdadero 3.141592
Hello 1 3.141592 Verdadero
Hello Verdadero 1 3.141592
Hello Verdadero 3.141592 1
Hello 3.141592 Verdadero 1
Hello 3.141592 1 Verdadero
1 Hello Verdadero 3.141592
1 Hello 3.141592 Verdadero
1 Verdadero Hello 3.141592
1 Verdadero 3.141592 Hello
1 3.141592 Verdadero Hello
1 3.141592 Hello Verdadero
Verdadero 1 Hello 3.141592
Verdadero 1 3.141592 Hello
Verdadero Hello 1 3.141592
Verdadero Hello 3.141592 1
Verdadero 3.141592 Hello 1
Verdadero 3.141592 1 Hello
3.141592 1 Verdadero Hello
3.141592 1 Hello Verdadero
3.141592 Verdadero 1 Hello
3.141592 Verdadero Hello 1
3.141592 Hello Verdadero 1
3.141592 Hello 1 Verdadero
Count 24
</pre>
Line 8,641 ⟶ 9,893:
===Recursive===
{{trans|Kotlin}}
<
permute = Fn.new { |input|
if (input.count == 1) return [input]
Line 8,659 ⟶ 9,911:
var perms = permute.call(input)
System.print("There are %(perms.count) permutations of %(input), namely:\n")
perms.each { |perm| System.print(perm) }</
{{out}}
Line 8,677 ⟶ 9,929:
{{libheader|Wren-math}}
Output modified to follow the pattern of the recursive version.
<
var input = [1, 2, 3]
Line 8,703 ⟶ 9,955:
}
System.print("There are %(perms.count) permutations of %(input), namely:\n")
perms.each { |perm| System.print(perm) }</
{{out}}
Line 8,715 ⟶ 9,967:
[3, 1, 2]
[3, 2, 1]
</pre>
===Library based===
{{libheader|Wren-perm}}
<syntaxhighlight lang="wren">import "./perm" for Perm
var a = [1, 2, 3]
System.print(Perm.list(a)) // not lexicographic
System.print()
System.print(Perm.listLex(a)) // lexicographic</syntaxhighlight>
{{out}}
<pre>
[[1, 2, 3], [1, 3, 2], [2, 1, 3], [2, 3, 1], [3, 2, 1], [3, 1, 2]]
[[1, 2, 3], [1, 3, 2], [2, 1, 3], [2, 3, 1], [3, 1, 2], [3, 2, 1]]
</pre>
=={{header|XPL0}}==
<
def N=4; \number of objects (letters)
char S0, S1(N);
Line 8,742 ⟶ 10,010:
[S0:= "rose "; \N different objects (letters)
Permute(0); \(space char avoids MSb termination)
]</
Output:
Line 8,774 ⟶ 10,042:
=={{header|zkl}}==
Using the solution from task [[Permutations by swapping#zkl]]:
<
L("rose","roes","reos","eros","erso","reso","rseo","rsoe","sroe","sreo",...)
Line 8,781 ⟶ 10,049:
zkl: Utils.Helpers.permute(T(1,2,3,4))
L(L(1,2,3,4),L(1,2,4,3),L(1,4,2,3),L(4,1,2,3),L(4,1,3,2),L(1,4,3,2),L(1,3,4,2),L(1,3,2,4),...)</
|